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Full text of "Report of the British Association for the Advancement of Science"

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REPORT 



OF THE 



FIFTY-FIFTH MEETING 



OP THE 



BRITISH ASSOCIATION 



FOR THE 



ADVMCEMENT OF SCIENCE; 



HELD AT 



ABERDEEN IN SEPTEMBER 1885. 




LONDON : 
JOHN MURRAY, ALBEMARLE STREET. 

1886. 

Office of tne Association : 22 Albemarle Steeet, London, W. 



PRINTED BY 

8P0TTI8W00DE AND CO., NEW-STEBET SQUARE 

LONDO.V 



CONTENTS. 



Page 

Objects and Rules of the Association xxyii 

Places and Times of Meeting and Officers from commencement xxxy i 

Presidents and Secretaries of the Sections of the Association from com- 
mencement xUii 

Evening Lectures Ivii 

Lectures to the Operative Classes Ix 

Officers of Sectional Committees present at the Aberdeen Meeting Ixi 

Treasurer's Account Ixiii 

Table showing the Attendance and Receipts at the Annual Meetings Ixiv 

Officers and Council, 1885-86 Ixvi 

Report of the Council to the General Committee livii 

Tlecommendations adopted by the General Committee for Additional 

Reports and Researches in Science Ixxi 

Synopsis of Grants of Money Ixxix 

Places of Meeting in 1886 and 1887 Ixxx 

jeneral Statement of Sums which have been paid on account of Grants 

for Scientific Purposes Ixxxi 

rrangement of theGeneral Meetings xcii 

i-ddress by the President, the Right Hon. Sir Lyon Platfaie, K.C.B., M.P., 
F.R.S 1 



* 



EEPORTS ON THE STATE OF SCIENCE. 

Report of the Committee, consisting of Professor G. Carey Foster, Sir W. 
Thomson, Professor Ayrton, Professor J. Perry, Professor W. G. Adaks, 
Lord Rayleigh, Dr. 0. J. LpDGE, Dr. John Hopkinson, Dr. A. Mtjirheab, 
Mr. W. H. Preece, Mr. H. Taylor, Professor Everett, Professor Schus- 
ter, Dr. J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glaze- 
brook (Secretary), Professor Chrystal, Mr. H. Tomlinson, and Professor 
W. Garnett, appointed for the purpose of constructing and issuing practical 
Standards for use in Electrical Jleasurements 31 

Report of the Committee, consisting of Professors A. Johnson (Secretary), J. 
G. MacGregoh, J. B. Cherriman, and H. T. Botey and Mr. C. Carpmael, 
appointed for the purpose of promoting Tidal Observations in Canada 8u 

A3 



IV CONTENTS. 

Page 

Fifth Report of the Committee, consisting of Mr. John Murkat (Secretary), 
Professor Schttster, Professor Sir William Thomson, Professor Sir H. E. 
RoscoE, Professor A. S. IIerschel, Captain W. de W. Abnet, Professor 
Bonnet, Mr. R. H. Scott, and Dr. J. H. Gladstone, appointed for the pur- 
pose of investigating the practicability of collecting and identifying Meteoric 
Dust, and of considering the question of undertaking regular observations 
in various localities 34 

Third Report of the Committee, consisting of Professors G. H. Darwin and 
J. C. Adams, for the Harmonic Analysis of Tidal Observations. Drawn 
up by Professor G. H. Darwin 35 

Report of the Committee, consisting of Mr. Robert H. Scott (Secretary), 
Mr. J. Norman Lockter, Professor G. G. Stokes, Professor Balfour 
Stewart, and Mr. G. J. Stmons, appointed for the purpose of co-operating 
with the Meteorological Society of the Mauritius in their proposed publica- 
tion of Daily Synoptic Charts of the Indian Ocean from the year 1861. 
Drawn up by Mr. R. H. Scott 60 

Rejjort of the Committee, consisting of Mr. James N. Shoolbred (Secre- 
tary) and Sir William Thomson, appointed for the reduction and 
tabulation of Tidal Observations in the English Channel, made with the 
Dover Tide-gauge ; and for connecting them with Observations made on the 
French coast 60 

Report of the Committee, consisting of Professor G. Forbes (Secretary), 
Captaiu Abnet, Dr. J. IIopkinson, Professor W. G. Adams, Professor 
G. C. Foster, Lord Ratleigh, Mr. Preece, Professor Schuster, Professor 
Dewar, Mr. A. Veknon Harcourt, and Professor Atrton, appointed for 
the purpose of reporting on Standards of "V\'hite Light. Drawn up by 
Professor G. Forbes 61 

Second Report of the Committee, consisting of Professor Balfour Stewart 
(Secretary), Mr. J. Knox Laughton, Mr. G. J. Symons, Mr. R. H. Scott, 
and Mr. Johnstone Stoney, appointed for the purpose of co-operating with 
Mr. E. J. Lowe in his project of establishing a Meteorological Observatory 
near Chepstow on a permanent and scientific basis 64 

Report of the Committee, consisting of Professor Balfour Stewart 
(Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick Evans, 
Professor G. H. Darwin, Professor G. Chrystal, Professor S. J. Perry, 
Mr. C. H. Caepmael, and Professor Schuster, appointed for the purpose of 
considering the best means of Comparing and Reducing Magnetic Observa- 
tions. Drawn up by Professor Balfour Stewart 65 

Report of the Committee, consisting of Professor Crum Brown (Secretary), 
Mr. MiLNE-HoME, Mr. John Murray, and Mr, Buchan, appointed for the 
purpose of co-operating with the Scottish Meteorological Society in making 
Meteorological Observations on Ben Nevis 90 

Seventeenth Report of the Committee, consisting of Professor Everett, Pro- 
fessor Sir AV. Thomson, Mr. G. J. Symons, Sir A. C. Ramsay, Dr. A. 
Geikib, Mr. J. Glaisher, Mr. Pengellt, Professor Edward Hull, 
Professor Prestwich, Dr. C. Le Neve Foster, Professor A. S. Herschel, 
Professor G. A. Lebour, Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F. 
Deacon, Mr. E. Wexhered, and Mr. A. Strahan, appointed for the 
purpose of investigating the Rate of Increase of Underground Temperature 
downwards in various Localities of Dry Land and under Water. Drawn 
up by Professor Everett (Secretarj-) 93 

Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S — 97 

Second Report of the Committee, consisting of Professor Schuster (Secretary), 
Professor Balfour Stewart, Professor Stokes, Mr. G. Johnstone Sxoney, 
Professor Sir H. E. RoscoE, Captain Abney, and Mr. G. J. Symons, ap- 
pointed for the purpose of considering the best methods of recording the 
direct Intensity of Solar Radiation 56 



CONTENTS. V 

Page 
Report on Optical Theories. By R. T. Glazebrook, M.A., F.R.S 157 

Report of the Committee, consisting of Professors Ramsay, Tilden, Mar- 
shall, and W. L. Goodwin (Secretary), appointed for the purpose of 
investigating certain Physical Constants of Solution, especially the Expan- 
sion of Saline Solutions 261 

Third Report of tlie Committee, consisting of Professors Williamson, Dewar, 
Feankland, Crum Brown, Obling, and Armstrong, Drs. Hugo Muller, 
r. R. Japp, and H. Forster Morlex, and Messrs. A. G. Vernon Har- 
coFRT, C. E. Groves, J. Millar Thomson, H. B. Dixon (Secretary), and 
V. H. Velet, reappointed for the purpose of drawing up a statement of 
the varieties of Chemical Names which have come into use, for indicating 
the causes which have led to their adoption, and for considering what can 
be done to bring about some convergence of the views on Chemical Nomen- 
clature obtaining among English and foreign chemists 262 

Report of the Committee, consisting of Professors Odling, Huntington, and 
Hartley, appointed to investigate by means of Photography the Ultra- 
violet Spark Spectra emitted by Metallic Elements and their combinations 
under varying conditions. Drawn up by Professor W. N. Hartley, F.R.S. 
(Secretary) 276 

Report of the Committee, consisting of Professor Tilden, Professor W. 
Ramsay, and Dr. W. W. J. Nicol (Secretary), appointed for the purpose 
of investigating the subject of Vapour Pressures and Refractive Indices of 
Salt Solutions 284 

Report of the Committee, consisting of Professor Sir H. E. Roscoe, Mr. J. N. 
Lockyer, Professors Dewar, Wolcott Gibbs, Liveing, Schuster, and 
W. N. Hartley, Captain Abney, and Dr. Marshall Watts (Secretary), 
appointed for the purpose of preparing a new series of AVave-length Tables 
of the Spectra of the Elements and Compounds 288 

Thirteenth Report of the Committee, consisting of Professors J. Prestwich, 
W. Boyd Dawkins, T. McK. Hughes, and T. G. Bonney, Dr. H. W. 
Geosskey (Secretary), Dr. Deane, and Messrs. C. E. De Range, H. G. 
FoRDHAM, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and R. H. 
TiDDEMAN, appointed for the purpose of recording the position, height 
above the sea, lithological characters, size, and origin of the Erratic Blocks 
of England, Wales, and Ireland, reporting other matters of interest con- 
nected with the same, and taking measures for their preservation 322 

Third Report of the Committee, consisting of Mr. R. Etheridge, Dr. H. 
WooDAVARD, and Professor T. Rupert Jones (Secretary), on the Fossil 
Phyllopoda of the Palaeozoic Rocks 326 

Fifth Report of the Committee, consisting of Mr. R. Etheridge, Mr. Thomas 
Gray, and Professor John Milne (Secretary), appointed for the purpose 
of investigating the Earthquake Phenomena of Japan. Drawn up by the 
Secretary 362 

Eleventh Report of the Committee, consisting of Professor E. Hull, Dr. 
H. W. Ceosskey, Captain Douglas Galton, Professors J. Pkesiwich 
and G. A. Lebour, and Messrs. James Glaisher, E. B. Marten, G. H. 
Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox 
Steangways, T. S. Stooke, G. J. Symons, W. Toplet, Tylden-Wright, 
E. Wethered, W. Whitaker, and C. E. De Range (Secretary), ap- 
pointed for the purpose of investigating the Circulation of Underground 
Waters in the Permeable Formations of England and Wales, and the 
Quantity and Character of the Water supplied to various Towns and Dis- 
tricts from these Formations. Drawn up by C. E. De Range 380 



VI CONTENTS. 

Page- 
Eeport of the Committee, consisting of Mr. H. Batterman, Mr. F. AV. 
Rtjdler, and Dr. H. J. Johnston-Lavis, for the Investigation of the 
Volcanic Plieuomena of Vesuvius. Drawn up by H. J. Johnston-Lavis, 
M.D., F.G.S. (Secretary) 395 

Report of the Committee, consisting of i\L'. W. T. Blanfoed and Mr. J. S. 
Gaedxer (Secretary), on the Fossil Plants of the Tertiary and Secondary 
Beds of the United" Kingdom. Drawn up by Mr. J. S. Gaednee, F.G.S", 
F.L.S 396- 

Report of the Committee, consisting of Messrs. R. B. Grantham, C. E. De 
Rance, J. B. Redman, W. Toplet, W. Whitakee, and J. W. Woodall, 
Major-General Sir A. Claeke, Sir J. N. Douglass, Captain Sir F. 0. Evans, 
Admiral Sir E. Ommanney, Captain J. Parsons, Professor J. Peestavicu, 
Captain W. J. L. Whaeton, and Messrs. E. Easton, J. S. Valentine, and 
L. F. Vernon Haecottrt, appointed for the purpose of inquiring into the 
Rate of Erosion of the Sea-coasts of England and Wales, and the Influence 
of the Artificial Abstraction of Shingle or other Material in that Action. 
0. E. De Rance and "W. Topley, Secretaries ; the Report edited by W. 
Toplet 404 

Report of the Committee, consisting of Professor Rat Lankester, Mr. P. L. 
Sclater, Professor M. Foster, Mr. A. Sedgavick, Professor A. M. Mar- 
shall, Professor A. C. Haddon, Professor Moselet, and Mr. Peect- 
Sladen (Secretary), appointed for the purpose of arranging for the occu- 
pation of a Table at the Zoological Station at Naples 466' 

Report of the Committee, consisting of Professor McIvendeick, Professor 
Struthers, Professor Young, Professor McIntosh, Professor Alletne 
Nicholson, Professor Cossar Ewaet, and Mr. John Mxjrrat (Secretary), 
appointed for the purpose of promoting the establishment of a Marine 
Biological Station at Granton, Scotland 474 

Report of the Committee, consisting of Sir Lton Platfair, Professor IVIose- 
I.ET, Admiral Sir E. Ommanney, Mr. P. L. Sclater, and Mr. A. Sedgwick 
(Secretary), appointed to prepare a Report on the Aid given by the Do- 
minion Government and the Government of the United States to the 
encouragement of Fisheries, and to the investigation of the various forms 
of Marine Life on the coasts and rivers of North America 479' 

Report of the Committee, consisting of Professor Huxlet, Mr. Sclater, 
Mr. Howard Saunders, Mr. Thiselton Dter, and Professor Moselet 
(Secretary), appointed for the purpose of promoting the establishment of 
Marine Biological Stations on the coast of the United Kingdom 480' 

Report of the Committee, consisting of Dr. H. C. Soebt and Mr. G. R. Vine, 
appointed for the purpose of reporting on recent Polyzoa. Drawn up by 
Mi: G. R. Vine 481 

Third Report of the Committee, consisting of Sir J. Hooeee, Dr. Qunthbr, 
Mr. HowAED Saundees, and Mr. Sclatee (Secretary), appointed for the 
purpose of exploring Kilima-njaro and the adjoining mountains of Equa- 
torial Africa 681 

Report of the Committee, consisting of Mr. John Coedeaux (Secretary), 
Professor A. Newton, Mr. J. A. Haevie-Beown, Mr. William Eagle 
Claeke, Mr. R. M. Barrington, and Mr. A. G. More, appointed for the 
purpose of obtaining (with the consent of Master and Brethren of the 
Trinity House and the Commissioners of Northern and Irish Lights) 
observations on the Migration of Birds at Lighthouses and Ligh tvessels, 
and of reporting on the same 685- 



CONTENTS. Vll 

Page 
Eeport of the Committee, consistiog of General Sir J. H. Lefrot, Lieut.- 
Colonel GoDWiN-AtrsTEN-, Mr. W. T. Blajiford, Mr. Sclater, Mr. 
Carrtjthers, Mr. Thiselton-Dter, Professor Struthers, Mr. G. W. 
Bloxam, Mr. H. W. Bates (Secretary), Lord Alfred Ghtirchill, 
ilr. F. Galton, and Professor Moselet, appointed for the pui-pose of 
furthering the Exploration of New Guinea by making a grant to 
Mr. Forbes for the purposes of his expedition 690 

Report of the Committee, consisting of General Sir J. H. Lefrot, the Rev. 
Canon Carver, Mr. F. Galton, Mr. P. L. Sclater, Professor Moselet, 
Dr. E. B. Tilor, Professor Boyd Dawkins, Mr. G. W. Bloxam, and 
Mr. H. W. Bates (Secretary), appointed for the purpose of furthering the 
scientific examination of the country in the vicinity of Mount Roraima in 
Guiana, by making a grant to Mr. Everard F. im Thurn for the purposes of 
his expedition 6y0 

Report of the Committee, consisting of the Rev. Canon Tristram, the 
Rev. F. Lawrence, and Mr. James Glaisher (Secretary), appointed for 
the purpose of promoting the Sur\ey of Palestine 691 

Report of the Committee, consisting of Dr. J. H. Gladstone (Secretary), 
Mr. William Shaen, Mr. Stephen Bourne, Miss Ltdia Becker, Sir 
John Lubbock, Dr. H. "W. Crossket, Sir Richard Temple, Sir Henrt E. 
RoscoE, Mr. James Hetwood, and Professor N. Stoet Maskeltne, 
appointed for the purpose of continuing the inquiries relating to the 
teachbg of Science in Elementary Schools 692 

Report of the Committee, consisting of Sir Frederick Bramwell (Secre- 
tary), Professor A. "W. Williamson, Professor Sir William Thomson, Mr. 
St. John Vincent Dat, Sir F. Abel, Captain Douglas Galton, Mi-. E. H. 
Carbutt, Mr. Macrort, Mr. H. Trueman Wood, Mr. W. H. Barlow, 
Mr. A. T. Atchison, Sir R. E. Webster, Mr. A. Carpmael, Sir John 
Lubbock, Mr. Theodore Aston, and Mr. James Brunlees, appointed for 
the purpose of watcliing and reporting to the Council on Patent Legislation 695 

Report of 4he Committee, consisting of Dr. E. B. Ttloe, Dr. G. M. Dawson, 
General Sir J. H. Lefrot, Dr. Daniel Wilson, Mr. Horatio Hale, 
Mr. R. G. Haliburton, and Mr. Georgse W. Bloxam (Secretary), 
appointed for the pm-pose of investigating and publishing reports on the 
physical characters, languages, and industrial and social condition of the 
North-western Tribes of the Dominion of Canada 



Report to the Council of the Corresponding Societies Conxmittee, consistin"' 
of Mr. Francis Galton (Chairman), Professor A. W. Williamson^ 
Captain Douglas Galton, Professor Botd Dawkins, Sir Rawson Rawson, 
Dr. Gakson, Dr. J. Evans, Mr. J. Hopkinson, Professor Meldola 
(Secretary), Mr. W^hitaker, Mr. G. J. Stmons, and Mr. H. George 
Fobdham 708 

On Electrolysis. By Professor Oliver J. Lodge, D.Sc 723 

A Tabular Statement of the Dates at which, and the Localities where, 
Pumice or Volcanic Dust was seen in the Lidian Ocean in 1883-84. By 
Charles Meldeum, F.R.S 773 

List of Works on the Geology, Mineralogy, and Palseontology of Stafford- 
shire, Worcestershire, and Warvriickshire. By William Whitaker, B.A., 
F.G.S., Assoc.Inst.C.E 780 

On Slaty Cleavage and allied Rock-Structures, with special reference to the 
Mechanical Theories of theii- Origin. By Alfred Harkeb, M.A., F.G.S. ^^'^ 



VUl CONTENTS. 

Page 
On the Strength of Telegraph Poles. By W. H. Preece, F.E.S., 
M.Inst.O.E 853 

On the Use of Index Numbers in the Investigation of Trade Statistics. By 
Stephen Bourne, F.S.S 859 

The Forth Bridge Works. By Andrew S. Biggart, C.E 873 

Electric Lighting at the Forth Bridge Works. By James N. Shoolbred, 
B.A., M.Inst.O.E 879 

The New Tay Viaduct. By Crawford Barlow, B.A., M.InstO.E 883 



TEANSACTIONS OF THE SECTIONS. 



Section A.— MATHEMATICAL AND PHYSICAL SCIENCE. 

THURSDAY, SEPTEMBER 10. 

Page 

Address bj- Professor G. Chrtstal, M.A., F.R.S.E., President of the Section 889 

1. On the Dilatancy of Media composed of Eigid Particles in Contact. By 
Professor Osborne Reynolds, M.A., F.R.S 896 

2. On Calculating the Surface Tension of Liquids by means of Cylindrical 
Drops or Bubbles. By Professor G. PiRiE, M.A 898 

3. On the Suiface Tension of Water which contains a Gas dissolved ia it. 

By Professor G. Pieie, M.A 898 

4. Thermod-\-namic Efficiency of Thermopiles. By Lord Ratleigf, D.C.L., 
LL.D., F.R.S 898 

6. On the Measm-ement of the Intensity of the Horizontal Component of the 
Earth's Magnetic Field. By Thomas Gray, B.Sc, F.R.S.E 898 

6. On Atmospheric Electricity. By Professor C. Michie Smith, B.Sc, 
F.R.S.E 899 

7. Molecular Distances in Galvanic Polarisation. By Professor J. Larmor, 
M.A 900 

8. On the Employment of Mance's Method for eliminating the Effects of 
Polarisation, to determine the Resistance of the Human Body. Bv Dr. 

W. H. SxoNE, M.A .' 900 

9. On Contact Electricity in Common Air, Vacuum, and different Gases. By 

J. T. BoTTOMLEY, M.A., F.R.S.E 901 

10. On a Specimen of almost Unmagnetisable Steel. By J. T. Bottomlet, 
M.A., F.R.S.E 903 

11. On the Cooling of Wires in Air and in Vacuum. By J. T. Bottomlet, 
M.A., F.R.S.E 904 

FBIDAY, SEPTEMBER 11. 

1. On Kinetic Theories of Matter. By Professor A. CRinu: Brown, 
M.D., F.R.S 904 

2. On Kinetic Theories. By Professor G. D. Liveing, M.A., F.R.S 904 

3. On Thermal Effusion and the Limiting Pressure in Polarised Gas. By 

G. JoHNSTONi! Stoney, LL.D., F.R.S 904 

4. On a Law concerning Radiation. By Professor Schuster, Ph.D., F.R.S. 905 

5. On Boltzmaun's Theorem. By Professor W. M. Hicks, M.A., F.R.S. ... 905 



X co:ntEiNts. 

Page 

6. The Rate of Explosion of Hydrogen and Oxygen. By H. B. Dixon, M.A. 905 

7. Report of the Committee for constructing and issuing practical Standards 

for use in Electrical Measurements 905 

8. Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S. 905 

9. On Constant Gravitational Instruments for measuring Electric Currents 

and Potentials. By Professor Sir W. Thomson, LL.D., F.R.S 905 

10. On a method of multiplying Potential from a hundred to several thousand 

Volts. By Professor Sir William ThomsOxV, LL.D., F.R.S 907 

11. On a form of Mercury Contact Commutator of Constant Resistance for use 

in adjusting Resistance Coils by Wheatstone's Bridge, and for other 
purposes. By Professor J. Viriamu Jones 907 

12. On Slide Resistance Coils -with ftlercury Contacts. By Professor J. 
ViBiAMTT Jones 907 

13. On the relative Merits of Iron and Copper Wire for Telegraph Lines. By 

W. H. Peeece, F.R.S 907 

SATURDAY, SEPTEMBER 12. 

1. On Orthoptic Loci. By the Rev. C. Taylor, D.D 909 

2. On the Reduction of Algebraical Determinants. By "\V. H. L. Russell, 

F.R.S 910 

3. Account of the Levelling Operations of the Great Trigonometrical Survey 

of India. By Major A. W. Baikd, R.E., F.R.S 911 

4. A Theorem relating to the Time-moduli of Dissipative Systems. By Lord 
Ratleigh, D.C.L., LL.D., F.R.S 911 

5. On a new Polariser devised by Mr. AJirens. By Professor Silvanits P. 
Thompson, D.Sc 912 

6. On a simple Modification of the Nicol Prism giving "Wider Angle of Field. 

By Professor Silvanus P. Thompson, D.Sc 912 

7. On some of the Laws which regulate the Sequence of Mean Temperature 
and Rainfall in the Climate of London. By II. Coitrtenat Fox, M.R.C.S. 912 

8. Notes upon the Rotational Period of the Earth and Revolution Period of 
the Moon deduced from the Nebular Hypothesis of Laplace. By W. F. 
Stanley, F.G.S., F.R.M.S 915 

9. On a Galvanic Battery. By C. J. Burnett 916 

MONDAY, SEPTEMBER U. 

1. Report of the Committee on Standards of White Light 916 

2. Photometry with the Pentane Standard. By A. Vernon Harcouet, 

M.A., F.R.S 916 

3. On a Photometer made with Translucent Prisms. By J. Joly, B.E 917 

4. Report of the Committee for reducing and tabulating the Tidal Obser- 
vations in the English Channel, made with the Dover Tide-gauge ; and 

for connecting them with Observations made on the French coast 917^ 

5. Seventeenth Report of the Committee on Underground Temperature 917 

6. Fifth Report of the Committee on Meteoric Dust 917 

7. A Tabular Statement of the Dates at which, and the Localities where, 

Pumice or Volcanic Dust was seen in the Indian Ocean in 1883-84. By 
Charles Meldrum, F.R.S 917" 



CONTENTS. xi 

8. Eeport of the Committee for co-operating with the Meteorological Society 
of the Mauritius in their proposed publication of Daily Synoptic Charts 

of the Indian Ocean from the year 1861 917 

9. Daily Synoptic Charts of the Indian Ocean. By Charles Meldexjjt, F.E.S. 917 
10. Eeport of the Committee appointed to co-operate with the Scottish 

Meteorological Society in making Meteorological Observations on Ben 



Nevis 



917 



11. On the Meteorology of Ben Xevis. By Alexander Buchan 917 

12. On some Eesults of Observations with kitewire-suspended Anemometers 

up to 1,300 feet above ground, or 1,800 feet above sea-level, in 1883-85. 
By E. Douglas Archibald 9^9 

13. On the Measurement of the Movements of the Ground, with reference to 
proposed Earthquake Observations on Ben Nevis. Bv Professor J \ 
EwiNG, B.Sc, F.E.S.E \' ' 920 

14. On the supposed Change of Climate in the British Isles within recent 
years. By Thomas Heath,B.A 922 

15. On Malvern, Queen of Inland Health Eesorts, and on improved Hygro- 
metric Observations. By Professor C. Piazzi Smyth, F.E.S.E 922 

16. The Annual Eainfall of the British Islands. By Alexander Buchan ... 923 

17. Eemarkable Occurrence during the Thunderstorm of August 6, 1885, at 
Albrighton. By J. Bedford Elwell ? .',.., 924 

18. On a supposed Periodicity of the Cyclones of the Indian Ocean south of 

the Equator. By Charles Meldrum, F.E.S 926 

19. A new Wind Vane or Anemoscope, specially designed for the use of 

Meteorologists. By G. M. Whipple, B.Sc, F.E.A.S 926 

■ 20. On the Third Magnetic Survey of Scotland. By Professor T. E. Thorpe 

F.E.S., and A. W. Eucker, F.E.S ' 926 

TUESDAY, SEPTEMBER 15. 

1. Eeport of the Cormnittee for considering the best means of Comparing 

and Eeducing Magnetic Observations 928 

2. Eeport of the Committee for considering the best methods of recordino- 
the direct Intensity of Solar Eadiation ° 923 

3. On a means of obtaining constant known Temperatures. By Professor 

W. Eamsat, Ph.D., and Sydney Young, D.Sc 928 

4. On certain facts in Thermodynamics. By Professor W Eamsay Ph D 

and Sydney Young, D.Sc ' '928 

5. Eeport on Optical Theories. By E. T. Glazebrooe:, M.A., F.E.S 929 

6. On a Point in the Theory of Double Eefraction. By E. T. Glazebrook, 
M.A., F.E.S 929 

7. Exhibition of a Mechanical Model illustrating some propert'es of the 
Ether. By G. F. Fitzgerald, F.E.S 93O 

8. On the Constitution of the Luminiferous Ether on the Vortex Atom 
Theory. By Professor W. M. Hices, M.A., F.E.S 930 

9. On an improved Apparatus for Christiansen's Experiment. Bv Lord 
Eayleigh, D.C.L., LL.D., F.E.S 930 

10. Optical Comparison of Methods for observing small Eotations Bv Lord 
Eayleigh, D.C.L., LL.D., F.E.S 930 

11. On the Accuracy of Focus necessary for sensibly perfect Definition Bv 
Lord Eayleigh, D.C.L., LL.D., F.E.S .'....... 930 



XU CONTENTS 

Page 

12. On Electro-Optic Action of a Charged Franklin's Plate. By J. Kerb, 
LL.D 930 

13. On Magnetic Double Circular Refraction. By De Witt B. Brace, Ph.D. 931 

14. Determination of the Heliographic Latitude and Longitude of Sun-spots. 

By Professor A. W. Thomson 931 

WEDXESDAT, SEPTEMBER 16. 

1. On the Nature of the Corona of the Sun. By William Huqgins, D.C.L., 
LL.D., F.R.S 932 

2. On the Spectrum of the SteUa Nova visible on the Great Nebula in An- 
dromeda. By William HuGsiNs, D.C.L., LL.D., F.R.S 935 

3. On the Bright Star iu the Great Nebula in Andromeda. By Ralph 

COPELAND, Ph.D 935 

4. On Solar Spectroscopy in the Infra Red. By Dr. Daniel Draper 936 

^. The Errors of Sextants as indicated by the Records of the Verification 
Department of the Kew Observatory, Richmond, Surrey. By G. M. 
Whipple, B.Sc, F.R.A.S ". 936 

6. On the Behaviour of First-class Watches whilst undergoing tests in the 
Rating Department of the Kew Observator}-, Richmond, Surrey. By G. 

M. Whipple, B.Sc, F.R.A.S 937 

7. On a recent Improvement in the Construction of Instruments graduated 
upon Glass. By G. M. Whipple, B.Sc, F.R.A.S 937 

8. On Methods of preventing Change of Zero of Thermometers by Age. By 

G. M. Whipple, B.Sc, F.R.A.S 938 

9. On a new and simple form of Calorimeter. By Professor W. F. Barrett 938 

10. On a modification of the Dauiell Battery, using Iron as Electropositive 
Element. By J. J. Coleman 938 

11. On a new form of Galvanometer. By Professor James Bltth, M.A., 
F.R.S.E 939 

12. On the Physical Conditions of Water in Estuaries. By Hugh Robert 
Mill, B.Sc, F.R.S.E., F.C.S 940 

13. Further Experiments in Photo-Electricity. By Professor Minchin 940 

14. On the Formation of a Pui-e Spectrum by Newton. By G. Griffith, 
M.A 940 

16. On the Use of Bisulphide of Carbon Prisms for cases of Extreme Spectro- 
scopic Dispersion, by Professor C. Piazzi Smyth ; and their Results in 
Gaseous Spectra, commented on by Professor Alexander S. IIerschel, 
M.A., F.R.S 942 

Section B.— CHEMICAL SCIENCE. 
THURSDAT, SEPTEMBER 10. 

Address by Professor H. E. Armstrong, Ph.D., F.R.S., Sec.C.S., President 

of the Section 946 

1. Report of the Committee appointed for the purpose of investigating by 
means of Photography the Ultra- Violet Spark Spectra emitted by Metallic 
Elements and their combinations under varying conditions 965 

2. On the Non-existence of Gaseous Nitrous Anhydride. By Professor 
William Ramsay, Ph.D., and J. Tudor Cundall 965 



CONTENTS. Xlll 

Page 

3. On some Actions of a Groves's Gas-battery. By Professor William 
Kamsat, Ph.D 965 

4. On the Spontaneous Polymerisation of Volatile Hydrocarbons at tlie 
ordinary atmospheric temperature. By Professor Sir Henet E. Roscoe, 
F.R.S.1 967 

5. On some new Vanadium Compounds. By J. T. Brieelet 968 

FRIDAY, SEPTEMBER 11. 

1. On the Essential Elements of Plants. By T. Jamieson 969 

2. The Periodic Law, as illustrated by certain physical properties of Organic 

Compounds. By Professor Thos. Caenellt, D.Sc 969^ 

3. Suggestions as to the Cause of the Periodic Law and the Nature of the 
Chemical Elements. By Professor Thos. Caenellt, D.Sc 969 

4. On the Value of the Refraction Goniometer in Chemical work. By Dr. 

J. H. Gladstone, F.R.S 970 

5. On the Refraction of Fluorine. By Geoege Glabstone, F.C.S 970 

6. Note on some Conditions of the Development, and of the Activity, of 
Chlorophyll. By Profe.ssor J, H. Gilbebt, LL.D., F.R.S 970 

7. A Plea for the Empiric Naming of Organic Compounds. By Professor 

Odling, F.R.S 972 

8. On the Action of Sodium Alcoholates on Fumaric and Maleic Ethers. By 
Professor Pttrdie, Ph.D., B.Sc 972 

9. On Sulphine Salts derived from Ethylene Sulphide. By Okste Masson, 
M.A., D.Sc 974 

10. An apparently new Hydrocarbon distilled from Japanese Petroleimi. By 

Dr. DivEES and T. Nakamuea 975 

11. Description of some new Crystallised Combinations of Copper, Zinc, and 

Iron Sulphates. By John Spillee, F.C.S 976 

SATURDAY, SEPTEMBER 12. 

1. The Composition of Water by Volume. By A. Scott, M.A., D.Sc 
F.R.S.E 976 

2. Description of a new Mineral from Loch Bhruithaich, Inverness-shire. 

By W, IvisoN Macadam, F.C.S., and Thomas Wallace 977 

3. Exhibition and Description of the apparatus employed in obtaining Oxygen 

and Nitrogen from the Atmosphere. Description of method used in 
converting Atmospheric Nitrogen into Ammonia. By Messrs. Bein 
Brothers 977 

MONDAY, SEPTEMBER 14. 

1. Report of the Committee on Chemical Nomenclature 977 

2. On Electrolysis. By Professor Olivee J. Lodge, D.Sc 977 

3. On Helmholtz's views on Electrolysis, and on the Electrolysis of Gases. 

By Professor Schustee, F.R.S 977 

4. On the Determination of Chemical Affinity in terms of Electromotive 

Force. By 0. R. Aldee Weight, D.Sc, F.R.S 973. 

o. On the Sensitiveness to Light of Selenium and Sulphur Cells. By Shel- 
EOED BiDWELL, M.A., LL.B 98L 



Xiv CONTENTS. 

Page 

6. On the Generation of a Voltaic Current by a Sulphur Cell with a Solid 
Electrolyte. By Shelford Bidwell, M.A., LL.B 982 

7. A Theory of the Connection between the Crystal Form and the Atom 

Composition of Chemical Compounds. By William Baelow 983 

S. On the use of Sodium or other soluble aluminates for softening and purify- 
ing bard and impure water and deodorising and precipitating sewage, 
waste water from factories, &c. By F. Maxwell Ltte, F.C.S 984 

TUESDAY, SEPTEMBER 15. 

1. Report on Vapour Pressures and Refractive Indices of Salt Solutions 985 

2. Report on certain Physical Constants of Solution 985 

3. On Solutions of Ozoue and the Chemical Actions of Liquid Oxygen. Bv 
Professor Dewak, F.R.S .". 985 

4. On Physical Molecular Equivalents. By Professor Guthrie, F.R.S 985 

5. The Size of Molecules. By Professor A. W. Reinold, M.A., F.R.S 986 

6. An approximate determination of the Absolute. Amounts of the Weights 

of the Chemical Atoms. By G. Johnstone Stoxet, D.Sc, F.R.S 987 

7. On Macromolecules (^lolecules of Matter in the CJrystalline State as dis- 

tinct from the Chemical Molecule), and determinations of some of them. 
By G. Johnstone Stonet, D.Sc, F.R.S 988 

8. On the Dilatancy of Media composed of Rigid Particles in Contact. By 
Professor Osborne Reynolds, M.A., F.R.S 989 

9. On the Evidence deducible from the Study of Salts. By Spencer U. 
Pickering 989 

10 On the Molecular Weights of Solids and Salts in Solution. By Professor 
W. A. TiLDEN, D.Sc, F.R.S 990 

11. On the Moleculai- Constitution of a Solution of Cobaltous Chloride. By 

Professor W. J. Rtissell, Ph.D., F.R.S 991 

WEDNESDAY, SEPTEMBER 16. 

1. An Electro-centrifugal ^Machine for Laboratory use. By Alexander 

Watt, F.I.C, F.C.S 991 

2. Barium Sulphate as a Cementing Material in Sandstone. By Professor 
Frank Clowes, D.Sc 992 

3 An Apparatus for determining the Viscosity of Oils. By A. H. Allen, 
F.C.S 992 

4. The Action of Nitrous Gases upon Amyl Alcohol. Bv J. Williams, 
F.C.S., F.I.C, and Mtles H. Smith, F.C.S .". 992 

6. On the Action of Water on Lead. By A. II. Allen, F.C.S 993 

Section C— GEOLOGY. 

THURSDAY, SEPTEMBER 10. 

Address by Professor J. W. Jtjdd, F.R.S., Sec.G.S., President of the Section 994 

1. Report on the Volcanic Phenomena of Vesuvius 1013 

2. Fifth Report on the Earthquake Phenomena of Japan 1013 

3. On some recent Earthquakes on the Durham Coast, and their probable 
cause. By Professor G. A. Lebotjr, M.A., F.G.S 1013 



CONTENTS. IV 

Page 

4. Notice of an Outline Geological Map of Lower Egj-pt, Arabia Petrsea, 

and Palestine. By Professor Edward Hull, LL.D., F.R.S., F.G.S. ... 1015 

5. On the Occurrence of Lower Old Red Conglomerate in the Promontory 
of the Fanad, North Donegal. By Professor Edward Hull, LL.D., 
F.R.S., F.G.S 1016 

6. On Bastite-Serpentine and Troktolite in Aberdeenshire ; with a Note on 

the Rock of the Black Dog. By Professor T. G. Bonnet, D.Sc, LL.D., 
F.R.S., Pres.G.S 1016 

7. On certain Diatomaceous Deposits (Diatomite) from the Peat of Aber- 
deenshire. By W. Iyison Macadam, F.G.S., F.I.G 1017 

8. List of Works on the Geology, Mineralogy, and Palaeontology of Stafford- 
shire, Worcestershire, and Warwickshire. Bv W. Whitaker, B.A., 
F.G.S., AssocInst.O.E '. 1017 

FRIDAT, SEPTEMBER IL 

1. The Volcanoes of Auvergne. By Tempest Anderson, M.D., B.Sc 1017 

2. On the Re-discovery of lost Numidiaii Marbles in Algeria and Tunis. 

By Lieut.-Colonel R. L. Platfair 1018 

3. Second Report on the Rate of Erosion of the Sea-coasts of England and 
Wales 1018 

4. The Chasm called the Black Rock of Kiltearn. By William Watson 1018 

5. The Bass of Inverurie, a fragment of an ancient Alluvial Bed. By the 

Rev. John Davidson, D.D 1018 

6. Thirteenth Report on the Erratic Blocks of England, Wales, and Ireland 1019 

7. The Direction of Glaci;ition as ascertained by the Form of the Striae. 

By Professor H. Carvill Lewis 1019 

8. Proposed Conditions to account for a former Glacial Period in Great 
Britain, existing under similar meteorological conditions to those that 

rule at the present time. By W. F. Stanley, F.G.S., F.R.M.S 1020 

9. On the Fyunon Beuno and Cae Gwyn Bone-Caves, North Wales. By 

H. Hicks, M.D., F.R.S., F.G.S 1021 

10. Note on Specimens of Fish from the Lower Old Red Sandstone of For- 
farshire. By the Rev. Hugh Mitchell 1023 

SATURDAY, SEPTEMBER 12. 

1. The Elgin Sandstones. By J. Gordon Phillips 1023 

2. Preliminary Note on a new Fossil Reptile recently discovered at New 

Spy nie, near Elgin. By Dr. R. H. Tkaquaik, F.R.S 1024 

3. Report on the Fossil Plants of tbe Tertiary and Secondary Beds of the 

United Kingdom 1025 

MONDAY, SEPTEMBER 14. 

1. The Highland Controversy in British Geology: its Causes, Course, and 

Consequences. By Professor Charles Lapworth, LL.D., F.G.S 1025 

2. The Geology of Durness and Eriboll, with special reference to the High- 

land Controversy. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S. E. 1027 

-3. Preliminary Note on some Traverses of the Crystalline District of the 
Central Alps. By Professor T. G. Bonnet, D.Sc, LL.D., F.R.S., 
Pres. G.S 1027 



xvi CONTENTS. 

Page 

4. Some Examples of Pressure-Fluxion in Pennsylvania. By Professor 

H. Cakvlll Lewis 1029 

5. On Slaty Cleavage and allied Rock Structures, with special reference to 
the Mechanical Theories of their Origin. By Alfred Haeker, M.A., 
F.G.S 1030 

6. On Irish Metamorphic Rocks. By G. Henry Kinahan, M.R.I.A lOSO' 

7. On Rocks of Central Caithness. By John^ Gtjnn 1030 

8. On some Rock Specimens from the Islands of the Fernando Noronha 
Group. By Professor A. Renabd, LL.D., F.G.S 1031 

9. On the Average Density of Meteorites compared with that of the Earth. 

By the Rev. E. Hill, M.A., F.G.S 1031 

TUESDAY, SEPTEMBER 15. 

1. Notes on a recent Examination of the Geology of East Central Africa. 

By Professor Henrt Drummond, F.R.S.E., F.G.S 1032' 

2. Report on the Rocks collected by H. "W. Johnston, Esq., from the upper 
part of the Kilima-njaro Massiif. By Professor T. G. Boxnet, D.Sc, 
LL.D., F.R.S., Pres.G.S 1032 

3. Some Results of the CrystaUographic Study of Danburite. By Max 
Schuster '. 1033 

4. American Evidences of Eocene Mammals of the ' Plastic Clay ' Period. 

By Sir Richard Owex, K.0.B.,F.R.S., F.G.S 1033 

5. Discovery of Anurous Amphibia in the Jurassic Deposits of America. 

By Professor 0. C. Marsh 1033 

6. Third Report on the Fossil Phyllopoda of the Palaeozoic Rocks 1033 

7. On the Distribution of Fossil Fishes in the Estuariue Beds of the 

Carboniferous Formation. By Dr. Traquair 1033 

8. Some Results of a detailed Sur^-ey of the Old Coast-lines near Trondh- 
jem, Norway. By Hugh Miller, F.G.S 1033 

9. The Parallel Roads of Lochaber. By James Melvin 1035 

10. Further Evidence of the Extension of the Ice in the North Sea during the 

Glacial Period. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S.E.... 103(> 

11. Recent Advances in West Lothian Geology. By H. M. Cadell, B.Sc. 1037 

12. Barium Sulphate as a Cementing Material in Sandstone. By Professor 
Frank Clowes, D.Sc ". 1038 

13. Notes on Fuller's Earth and its applications. By A. C. G. Cameron ... 1039 

WEDNESDAY, SEPTEMBER 16. 

1. On the Glacial Deposits at Montrose. By Dr. Howden 1040 

2. Notes on the Rocks of St. Kilda. By Alexander Ross, F.G.S 1040 

3. Eleventh Report on the Circulation of Underground Waters in the Per- 
meable Formations of England and AVales, and the Quantity and 
Character of the Water supplied to various Towns and Districts from 
these Formations 1041 

4. On Deep Borings at Chatham : a Contribution to the Deep-seated Geology 

of the London Basin. By W. Whitaker,B.A., F.G.S., Assoc. Inst.C.E. 1041 

5. On the Waterworks at Goldstone Road, Brighton. By W. Whitaker, 
B.A., F.G.S., Assoc.Inst.C.E " 1041 



CONTENTS. XVll 

Section D.— BIOLOGY. 

THURSDAY, SEPTEMBER 10. 

Page 
Address by Professor W. 0. McIntosh, M.D., LL.D., F.R.S. L. & E., F.L.S., 
President of the Section 1043 

1. On the Tay Whale {Megaptera longimana) and other Whales recently 
ohtained in the district. By Professor Strtjthers, M.D., LL.D 1053 

2. Is the Commissural Theory of the Corpus Callosum correct ? By Pro- 

fessor D. J. Hamilton, M.B 1054 

3. The Evidence of Comparative Anatomy with regard to Localisation of 

Function in the Cortex of the Brain. By Alex. Hill, M.A., M.B., 
M.R.O.S 1054 

4. Report of the Committee for the Exploration of Kilima-njaro, and the 

adj oining Mountains of Eastern Equatorial Africa 1055 

5. Report of the Committee for arranging for the occupation of a Table at 

the Zoological Station at Naples 1055 

6. Report of the Committee for promoting the establishment of Marine 

Biological Stations on the coast of the United Kingdom 1056 

7. Report of the Committee for promoting the establishment of a Marine 

Biological Station at Granton 1056 

8. Report on recent Polyzoa 1056 

9. Report on the Record of Zoological Literature 1056 

10. Report on the Bibliography of certain Groups of Invertebrata 1056 

FRIDAY, SEPTEMBER 11. 

1. Recent Observations on the Habits and Instincts of Ants and Bees. By 

Sir John Lubbock, Bart., F.R.S 1056 

2. On the Carpal Bones in various Cetaceans. By Professor Strtjthers, 

M.D., LL.D 1056 

3. Account of the Dissection of the Rudimentary Hind-limb of Balcenoptera 
musculm. By Professor Strtjthers, M.D., LL.D 1056 

4. Some points in the Anatomy of Sowerby's Whale (Mesoplodon bidens). 

By Professor W. Turner, M.B., F.R.S 1057 

5. On the use of Graphic Representations of Life^histories in the teaching 

of Botany. By Professor F. 0. Bower 1057 

Supplementary Meeting. — Physiology. 

1. On the Direct Action of Anaesthetics on the Frog-heart. By J. 
McGregor-Robertson, M.A., M.B 1057 

2. On the Action of Cold on Microphytes. By John G. McKendrick, 

M.D., LL.D., F.R.S .' 1058 

3. On the Action of Ozonised Air upon Micro-Organisms and Albumen in 

Solution. By J. J. Coleman, F.C.S 1058 

4. A new Theory of the Sense of Taste. By Professor J. Berry 
Haycraft 1059 

SATURDAY, SEPTEMBER 12. 

1. On a Model of the Whale. By Captam Gray 1059 

2, On the Hybridisation of Salmonidae at Howietoun. By Francis Day, 

CLE 1059 

1885. 0, 



■xviii CONTENTS. 

Page 

3, On the Identification of the British Mosses by their Distinctive Cha- 

racters. B}^ Mrs. FAEatTHAESON, F.R.M.S 106?. 

4. On the Flora of Caithness. By James F. Grant 1063 

.5. On Chinese Insect White Wax. By A. Hosie 1064 

6. On the Existence of Cephalopoda in the Deep Sea. By W. E. Hoyle... 1064 

7. On the Echiuoderm Fauna of the Island of Ceylon. By Professor F. 
Jeffrey Bell, M.A., Sec.R.M.S '. 1065 

MONDAY, SEPTEMBER 14. 

1. Report on the Aid given by the Dominion Government and the Govern- 

ment of the United States to the encouragement of Fisheries, and to the 
investigation of the various forms of Marine Life on the coasts and 
rivers of North America 1065 

2. On the Size of the Brain in Extinct Animals. By Professor 0. C. Marsh 1065 

3. On the Systematic Position of the Chamseleon, and its Affinities with 

the Dinosauria. By Professor D'Aecy W. Thompson 1065 

4. On the Hind Limb of Ichthyosaurus, and on the Morphology of Verte- 
brate Appendages. By Professor DArcy W. Thompson 1065 

5 On the Origin of the Fishes of the Sea of Galilee. Bv Professor Edward 

Hull, LL.D.,F.R.S ." 1066 

Q, On the Cause of the Extreme Dissimilarity of the Faunas of the Red Sea 

and Mediterranean. By Professor Edward Hull, LL.D., F.R.S 1068 

7 On the Morphology of the Human Arterial System. Bv Professor 
A. MacAlister, F.R.S " 1068 

8. On the Viscera of Gymnotus electricus. By Professor Cleland, M.D., 
F.R.S 1068 

9. On the Spiracle of Fishes in its relation to the Head, as developed in the 
Higher Vertebrates. By Profe.«sor Cleland, M.D., F.R.S 1069 

10. On the Tail of Myxine glutinosa. By Professor Cleland, M.D., F.R.S. 1069 

11. On the Nucleus in the Frog's Ovum. By George Thin, M.D 1069 

12. On the Structure and Arrangements of the St. Andrews Marine 

Laboratory. By Professor McInxosh, M.D., LL.D., F.R.S 1071 

13. Remarks on the work at the St. Andrews Marine Laboratory during 

nine months. By Professor McIntosh, M.D., LL.D., F.R.S 1071 

14 On the Chemical Composition of the Milk of the Porpoise. Bv Professor 

PuRDiE, Ph.D., B.Sc '. 1072 

15. On certain processes formed bv Oerapus on Tubulana indivisa. By 
Professor McIntosh, M.D., LL.D., F.R.S .'. 1072 

16. On a new British Staurocephalus. By Professor McIntosh, M.D., F.R.S. 1073 

17. On certain remarkable Structures resembling Ova from Deep Water. 

By Professor McIntosh, M.D., LL.D., F.R.S 1073 

18. On the Ova of Callionymus lyra, L. (the Skulpin). By Professor 
McIntosh, M.D., LL.D., F.R.S 1073 

19. On the Zoocytium or Gelatinous Matrix of Ophrydium versatile. By 
Professor Allen Haeker, F.L.S 1074 

Supplementary Meeting. — Physiology. 

1. On the Action of Atropine on the Secretion of the Kidney, its Evidence 
as to the Mechanism of the Secretion. By J. McGregor-Robertson, 
M.A.,M.B 1075 



CONTENTS. xix 

Page 

2. On a Chemical Difference between Living and Dead Protoplasm. By 

Oscar Loew, Ph.D 1075 

3. A Comparative View of the Albuminous Substances contained in the 

Blood of Vertebrate and Invertebrate Animals. By W. D. Halli- 
BUETON, M.D., B.Sc, M.R.C.P 1077 

4. On the Striated Muscles in the Gills of Fishes. By Dr. J. A. 
McWiLLIAM 1077 

5. On the Structm-e of the Intestine in the Hedgehog and the Mole. By 

Dr. J. A. McWiLLiAM 1078 

6. On Plant-Digestion, especially as occurring in Carica papaya. By 
Sidney MARim, M.D., B.Sc, M.E.C.P 1078 

7. On a new kind of Colour Apparatus for Physiological Experiment. By 

John Aiken 1079 

8. On the Structure of Hyaline Cartilage. By Geoege Thin, M.D 1078 

9. The Preservation and Prolongation of Life to 100 years. By Protheeoe 
Smith, M.D 1079 

SUPPLEMENTAET MEETING. — BOTANT. 

1. On the Application of the Anatomical Method to the Determination 

of the Materials of the Linnean and other Herbaria. By Professor 

L. Radlkofer 1080 

2. On the Influence of Impregnation on a Plant. By E. J, Lowe, F.R.S.... 1081 

3. On the Impregnation of Composite Flowers. By E. J. Lowe, F.R.S. ... 1082 

4. On the Occurrence of Fungi in the Roots of Orchids. By J. Macmillan 1083 

5. Notes on Experiments as to the Formation of Starch in Plants under the 

influence of the Electric Light. By H. Marshall Ward 1086 

6. On the Flora of Banfishire. By the Rev. W. S. Bruce 1087 

7. On the Flora of Elgin. By James Mackenzie 1087 

8. On the Division and Conjugation of Spirogyra. By Dr. J. M. Macfar- 
LANE, F.R.S.E ". 1088 

9. On a Microscopic Fungus in Fossil Wood, from Bowling. By Dr. J. M. 
Macfarlane, F.R.S.E 1088 

10. On a new Method of preparing the Epidermal Tissues of Pitcher Plants. 

By Dr. J. M. Macfarlane, F.R.S.E 1088 

11. On Aberdeenshire Plants as Food for Animals. By William Wilson, 

jun 1088 

TUESDAY, SEPTEMBEE 15. 

1. Report on the Migration of Birds 1089 

"2. Note on the Intelligence of the Dog. By Sir John Lttbbock, Bart., F.R.S. 1089 

3. On the Development of the Food-fishes at the St. Andrews Marine 

Laboratory. By Edward E. Prince 1091 

4, On the Nest and Development of Gastrosteus gpinachia at the St. An- 

drews Marine Laboratory. By Edward E. Prince 1093 

.5. On the Reproduction of the Common Mussel (Myttlus ediUis, L.) By 

John Wilson IO94 

6. On the Modification of the Trochal Disc of the Rotifera. By Professor 

A. G. Bourne, D.Sc, F.L.S - IO95 

a 2 



XX CONTENTS. 

Page 

7. On Buddine- in the OligocliEeta. By Professor A. G. Bofene, D.Sc, 

F.L.S 109G 

8. Demonstration of a new Moneron. By Professor D'Arcy W. Thompsoi^ 1097 

9. On the Blastopore and MesoUast of Sabella. By Professor D'Arct W. 
Thompson 1097 

10. On the Annelids of the Genus Dero. By E. C. Botjsfield 1097 

11. On some little known Fresh-water Annelids. By E. C. Bousfield 1098 

12. On the Coloration of the Anterior Segments in the Malanidse. By Pro- 

fessor Allen II.VKKER, F.L.S 1098 

1.3. Systematique du genre Polygordius. By Julien Fraipont 1098 

14. On some of our Migratory Birds, as first seen in Aberdeenshire. By 

James Taylor 1098 

Supplementary Meeting. — Anatomy. 

1. On the Connection of the Os Odontoidium with the centrum of the axis 
vertebra. By Professor D. J. Cunningham, F.R.S 1101 

2. On the Curvature of the Spine in the Foetus and Child. By Dr. John- 

ston Symington 1101 

3. On the Bronchial Syrinx of the Cuculidse and Caprimulgidse. By Frank 

E. Beddard, M.A., F.R.S.E 1101 

4. Contributions to the Structure of the Oligochseta. By Frank E. Bed- 

dard, M.A., F.R.S.E 110^ 

5. On the Cervical Vertebrae in Balaina mysticetus, &c. By Professor 

Struthers, M.D., LL.D 1103 

6. On the Development of the Foot of the Horse. By Professor Struthers, 

M.D., LL.D '. llOa 

7. On the Development of the Vertebraj of the Elephant. By Professor 

Struthers, M.D., LL.D 110^ 

8. On the Kidneys of Gasteropoda and the Renal Duct of Paludina. By W. 

B. Benham 1103- 

Section E.— GEOGRAPHY. 

TIIUR.SDAY, SEPTEMBER 10. 

1. The Indian Forest School. By Major F. Bailey, R.E., F.R.G.S 1104 

2. Brazil. By Colin Mackenzie, F.R.G.S 1105 

3. On the Progress of African Philology. By R. Needham Cust, 

F.R.G.S '. ". 1105 

4. On the Changes which have taken place in Tunis since the French Pro- 

tectorate. By Lieut.-Colonel R. L. Playfaie 1105 

FRIDAY, SEPTEMBER IL 

Address by General J. T. Walker, C.B., R.E., LL.D., F.R.S., President of 

the Section HOC? 

1. The Indian Forest Survey. By Major F. Bailey, R.E., F.R.G.S 1121 

2. Account of the Levelling Operations of the Great Trigonometrical Survey 

of India. By Major A. W. Baied, R.E., F.R.S 112.3 

3. Notes on the Physiography of Southern India. By Colonel B. R. 

Bkanfill 112-1 



CONTENTS. XXI 

Page 

4. On a Trip from Upper Assam into the Kampti Country and the Western 

Branch of the Irrawady River, made by Colonel R. B. AVoodthorpe, 
R.E., and Major C. R. MacGregor. By Lieut.-Colonel H. H. Qodwin- 
Adsten, F.R.S 1126 

5. On the complete Exploration of Lake Yamdok in Tibet. By Tee- 

LAWNEX SaUNDEES 1126 

<3. On Himalayan Snow Peaks. By Lieut.-Colonel H. C. B. Taiinbr 1126 

7. Notes on recent Mountaineering in the Himalaya. By Douglas AV. 

Feeshfield, F.R.G.S 1127 

MONDAY, SEPTEMBER 14. 

1. Projected Restoration of the Reian Moeris, and the Province, Lake, and 

Canals ascribed to the Patriarch Joseph. By Cope Whitehouse, M.A. 1127 

2. Report of the Committee for furthering the Scientific Examination of the 

Country in the vicinity of Mount Roraima in Guiana 1128 

3. Mount Roraima. By Eveeard iii Thuen 1128 

4. Report of the Committee appointed for the purpose of promoting the 

Survey of Palestine 1128 

5. The Cadastral Survey of India. By Lieut.-Colonel W, Barron 1128 

6. The Ordnance Survey of Cyprus. By Teelawney Saunders 1129 

7. The Rivers of the Punjab. By General Robert Maclaqan,R.E 1129 

8. On a Clinometer to use vdth a Plane-Table. By Major Hill 1131 

9. On a supposed Periodicity of the Cyclones of the Indian Ocean, south of 

the Equator 1131 

10. The Portuguese Possessions in West Africa. By H. H. Johnston 1132 

11. North-west Australia, By J. G. Bartholomew 1132 

TUESDAY, SEPTEMBER 15. 

1. Antarctic Research. By Admiral Sir Erasmus OMMANNEr,C.B., F.R.S., 
F.R.G.S 1132 

2. Geogiaphical Education. By J. Scott Kelxie 1133 

3. On Overland Expeditions to the Arctic Coast of America. By John 
Rae, M.D., LL.D., F.R.S., F.R.G.S 1133 

4. On the best and safest Route by which to attain a High Northern 
Latitude. By John Rae, M.D., LL.D., F.R.S., F.R.G.S 1136 

5. Oceanic Islands and Shoals. By J. Y. Buchanan 1136 

6. On the Depth of the permanently Frozen Stratum of Soil in British 

North America. By General Sir J. Henet Lefeot, K.C.M.G., F.R.S. 1136 

7. On Recent Explorations in New Guinea. By Coutts Teotter 1136 

WEDNESDAY, SEPTEMBER 16. 

1. On Journeyings in South-western China. By A. Hosie 1137 

2. Notes on the large Southern Tributaries of the Rio Solimoes or Upper 
Amazon in Brazil, with special reference to the Rio Jutahi. By Pro- 
fessor J. W. H. Teail 1138 

3. The Depth and Temperature of some Scottish Lakes. By J. Y. 

Buchanan 1138 



XXll CONTENTS. 

Page 

4. On the Geographical Features of the Beauly Basin. By Tho. W. 
Wallace ll;38- 

5. What has been done for the Geography of Scotland, and what remams 

to he done. By H. A. Websteb 1138- 

6. On Bathy-hypsographical Maps, with special reference to a Comhination 

of the Ordnance and Admiralty Surveys. By E. G. Eavenstein, 
F.K.G.S.. 1140 

Section F.— ECONOMIC SCIENCE AND STATISTICS. 
THURSDAY, SEPTEMBER 10. 

1. Report of the Committee for continuing the inquiries relating to the 

teaching of Science in Elementary Schools 1141 

Address by Professor Henry Sidgwick, M.A., Litt.D., President of the 

Section 1141 

2. On the alleged Depression of Trade. By Professor Leone Levi, F.S.S... 11 ')5 

3. On the Variations of Price-Level since 1«50 By Michael G. IMulhall, 

F.S.S 1157 

FRIDAT, SEPT EM BE It 11. 

1. On the Municipalisation of the Land. By Sir George Campbell, 
K.CS.L, M.P 1158 

2. The Agriculture of Aberdeenshire. By Colonel Innes 1161 

3. The Agricultural Situation. By Professor W. Fream, B.Sc, F.L.S., 

F.G.S IIGI 

4. On recent Changes in Scottish Agriculture. By Major P. G. Craigie.,. 11G2 

SATURDAY, SEPTEMBER 12. 

1. On the International Forestry Exhibition. By Dr. Ceombie Brown ... 1164 

2. What is Capital ? By W. Westgarth 1165 

3. On Methods of afcertainiug Variations in the Rates of Birth, Death, and 
Marriage. By F. Y. Edgeworth 1165 

4. On the Application of Biology to Economics. By Patrick Geddes IIGG 

MONDAY, SEPTEMBER 14. 

1. On the Use of Index Numbers in the Investigation of Trade Statistics. 

By Stephen Bourne, F.S.S 1168 

2. On Depression of Prices and Results of Economy of Production, and on 

the Prospect of Recovery. By Hyde Clarke, F.S.S 1168 

3. On Customs Tarifls. By A. E. Bateman 1160 

4. How its Fiscal Policy may affect the Prosperity of a Nation. By 

Alexander Forbes 11 60 

3. On the Incidence of Imperial Taxation. By Dr. W. A. Hunter 1170 

TUESDAY, SEPTEMBER 15. 

1. State Guarantee of War Risks. By John Corry 1171 

2. On the British Standard of Value. By Dana Horton 1172 



CONTENTS. XXm 

Page 

3. Sliding Scales in the Coal Industry. By Professor J. E. C. Mttnro 1173 

4. Anomalies in the condition of Scotch Miners in contrast with other un- 
skilled Labourers. By William Small 1174 

6. The Statistics and some points in the Economics of the Scottish Fisheries. 

By William Wati, F.S.S 1175 

6. On the Pauperisation of Children by the Operation of the ' Scotch 

Education Act, 1872.' By Matthew Blair 1176 

WEDNESBAT, SEPTEMBER 16. 

1. Agricultural Investigation and Education. By Thomas Jamieson 1177 

2. Policy in Taxation. By J. B. Greig 1179 

3. A new view of the Consequences of Unpunctuality in Railway Trains. 

By Cornelius Walford, F.I.A., F.S.S 1180. 

4. On the Industrial Remuneration Conference. By the Rev. W. 
Cunningham, B.D 1181 

Section G.— MECHANICAL SCIENCE. 

THURSBAY, SEPTEMBER 10. 

Address by B. Baker, M.Inst.C.E., President of the Section 1182 

1. The New Tay Viaduct. By Crawford Barlow, B.A., M.Inst.C.E. ... 1192 

2. The Forth Bridge Works. By Andrew S. Bjggart, C.E 1193 

FRIBAY, SEPTEMBER 11. 

1. The American System of Oil Pipe Lines. By J. H. Harris 1193 

2. The Movement of Land in Aberdeen Bay. By W. Smith 1193 

3. On Shallow-draught Screw Steamers for the Nile Expedition. By 

J. T. Thornycroft, M.Inst.C.E 1193 

4. The Sphere and Roller Friction Gear. By Professor H. S. Hele Shaw 1193 

5. On the Employment of the Road Engine in Construction and Main- 

tenance of Roads. By Colonel Innes 1194 

MOXBAY, SEPTEMBER 14. 

1. Electric Lighting and the Law. By Dr. Leavis Edmunds 1195 

2. On an Electric Safety Lamp for Miners. By J. Wilson Swan, M.A.... 1196 

3. On the Strength of Telegraph Poles. By W. H. Preece, F.R.S., 
M.Inst.C.E 1197 

4. On Domestic Electric Lighting. By W. H. Preece, F.R.S., M.Inst.C.E. 1197 

5. On a System of Periodic Clock Control on Telephone or Telegraph Lines. 

By Professor W. F. Barrett, F.R.S.E 1198 

6. Electric Lighting at the Forth Bridge Works. By James N, Shool- 
bred, B.A., M.Inst.C.E 1198 

7. On the Development of the Pneumatic System as applied to Telegraph 
purposes. By J. W. Willmot 1198 

TTTESBAY, SEPTEMBER 15. 

1. Report of the Patent Law Committee 1199 

2. Autographic Apparatus for Machines for Testing Materials. By Pro- 

fessor W. C. Unwin, M.Inst.C.E 1199 



XXIV CONTENTS. 

Page 

3. Notes on Mild Steel. ByG.J. Goedon 1200 

4. The Diminution of Casualties at Sea. By Don Artfko de Maecoakttj 1201 

5. On the Deep Sea Channel into Swansea Harbour. By Robert Oappek 1202 

6. On the Spey Bridge at Garmouth and the River Spey. By P. M. 
Baenett 1203 

7. On a New Form of High Speed Friction Driving Gear. By Professor 

J. A. EwiNG ; 1203 

8. On Ashton's New Power Meter. By Professor H. S. Hele Shaw 1203 

9. On the British Association Standard Gauge for Small Screws. By 
Edwaed Rigg, M.A 1203 



Section H.— ANTHROPOLOGY. 

THURSDAY, SEPTEMBER 10. 

1. The Scope of Anthropology, and its relation to the Science of Mind. 

By Alexander Bain, LL.D 1204 

2. The Index of the Pelvic Brim as a Basis of Classification. By Professor 

W. TuENER, M.B., F.R.S 1205 

3. A Portable Scale of Proportions of the Human Body. By W. F. 

Stanley, F.G.S., F.K.M.S 1206 

Address by Francis Galton, M.A., F.R.S., President of the Anthropo- 
logical Institute, President of the Section 1206 

FRIDAY, SEPTEMBER 11. 

1. Insular Greek Customs. By J. Theodore Bent 1214 

2. On the Working of the Ancient Monuments Act of 1882. By General 
PiTT-RivERs, r.R.S 1214 

3. American Shell-work and its Affinities. By Miss A. W. Buckland ...1214 

4. Note on the Redmen about Roraima. By E. F. im Thtten 1215 

5. A Game with a History. By J. W. Crombie, M.A 1215 

6. The Rule of the Road from an Anthropological point of view. By Sir 
George Campbell, K.O.S.I 1215 

7. On the Modes of Grinding and Drying Corn in old times. By Miss Jeanie 

M. Laing 1216 

8. The Flint-knappers' Art in Albania. By A. J. Evans 1216 

9. The Discovery of Nauki-atis. By W. M. Flinders Petrie 1216 

MONDAY, SEPTEMBER 4. 

1. On Ancient Tombs in the Greek Islands. By J. Theodore Bent 1217 

2. A New Cave Man of Mentone. By Thomas Wilson 1218 

3. Happaway Cavern, Torquay. By William Pengellt, F.R.S., F.G.S. , 1219 

4. On the Human Remains found in Happaway Cavern, Torquav. By 

J. G. gaeson, m.d :. ....•; ;; 1220 

5. On Three Stone Circles in Cumberland, with some further observations 

on the relation of Stone Circles to adjacent hills and outlying stones. 

By A. L. Lewis, M.A.I ...Tf. 1220 



CONTENTS. XXV 

Page 

6. The Archaeological Importance of ancient British Lake-dwellings and 
their relation to analogous remains in Europe. By R. Munko, 
M.A., M.D 1221 

7. The Stone Circles in Aherdeenshire, -with special reference to those in 
the more Lowland parts of the County, their Extent and Arrangement, 
singly or in gi-oups, with General Observations. By the Rev. James 
Peter, F.S.A.Scot '. 1221 

8. Stone Circles in Aberdeenshire. By John Mtlne, M.A 1223 

9. Notes on a recent Antiquarian Find in Aberdeenshire. By Dr. F. Mait- 
LAND MoiB 1223 

10. The Picts and Prje-Celtic Britain. By Hyde Clarke 1223 

11. Report of the Committee for investigating and publishing reports on 
the physical characters, languages, and industrial and social condi- 
tions of the North-western Tribes of the Dominion of Canada 1224 

TUESDAY, SEPTEMBER 15. 

1. Notes on the opening of a Cist in the parish of Leslie, Aberdeenshire. 

By the Rev. John Russeu, M.A 1224 

2. Notes on a Cist found at Parkhill, Dyce, in October 1881. By W. 
Ferguson 1225 

3. On the Human Crania and other contents found in short stone Cists in 
Aberdeenshire. By Professor J. Struthers, M.D., LL.D 1225 

4. Notice of Human Bones found in 1884 in Balta Island, Shetland, by 

D. Edmonston, Esq. By Professor J. Struthers, M.D., LL.D 1225 

6. Some Important Points of Comparison between the Chimpanzee and 

Man. By Professor D. J. Cunningham 1226 

6. Abnormal and Arrested Development as an Indication of Evolutionary 
History. By J. G. Garson, M.D 1226 

7. The Symbol Pillars abounding in Central Aberdeenshire. Bv the Rev. 
John Davidson, D.D .* 1227 

8. Notes on some of the Bantu Tribes living round Lake Nyasa in Eastern 
Central Africa. By Dr. Robert Laws 1227 

9. Exhibition of the Skeleton of a Strandlouper from South Africa. By 
Professor A. Macalister, F.R.S 1228 

10. A brief Account of the Nicobar Islanders, with .special reference to the 
Inland Tribe of Great Nicobar. By E. H. Man 1228 

11. A proposed Society for Experimental Psychology. By Joseph Jacobs, 
B.A : 1230 

12. A Comparative Estimate of Jewish Ability. By Joseph Jacobs, B.A.... 1231 

13. Traces of Early Human Habitations on Deeside and Vicinity. By the 
Rev. J. G. Michie, A.M 1232 

Index 1233 



XXVI LIST OF PLATES. 



LIST OF PLATES. 



PLATES I., IL, AND III. 

Illustrating the Eeport of the Committee on the Fossil Plants of tlie Tertiary andl 
Secondary Beds of the United Kingdom. 

PLATE IV. 

Illustrating the Report ot the Committee on the Erosion of the Sea-coasts of 

England and Wales. 



PLATES V. AND Va. 

Illustrating Mr. Meldrum's Communication, ' A Tabular Statement of the Dates 
at which, and the Localities where. Pumice or Volcanic Dust was seen in the 
Indian Ocean in 1883-84.' 

PLATE VI. 

Illustrating Mr. Andrew S. Biggart's Communication, ' The Forth Bridge Works.' 

PLATE VII. 
Illustrating Mr. Crawford Barlow's Communication, ' The New Tay Viaduct.' 



OBJECTS AND RULES 



OF 



THE ASSOCIATION. 



OBJECTS. 

The Association contemplates no interference with the ground occupiedl 
by other institutions. Its objects are : — To give a stronger impulse and 
a more systematic direction to scientific inquiry, — to promote the inter- 
course of those who cultivate Science in different parts of the British 
Empire, with one another and with foreign philosophers, — to obtain a 
more general attention to the objects of Science, and a removal of any 
disadvantages of a public kind which impede its progress. 

RULES. 

Admission of Members and Associates. 

All persons who have attended the first Meeting shall be entitled to 
become Members of the Association, upon subscribing an obligation to 
conform to its Rules. 

The Fellows and Members of Chartered Literary and Philosophical 
Societies publishing Transactions, in the British Empire, shall be entitled,, 
in like manner, to become Members of the Association. 

The Officers and Members of the Councils, or Managing Committees, 
of Philosophical Institutions shall be entitled, in like manner, to become 
Members of the Association. 

All Members of a Philosophical Institution recommended by its Coun- 
cil or Managing Committee shall be entitled, in like manner, to become 
Members of the Association. 

Persons not belonging to such Institutions shall be elected by the- 
General Committee or Council, to become Life Members of the Associa- 
tion, Annual Subscribers, or Associates for the year, subject to the 
approval of a General Meeting. 

Compositions, Subscriptions, and Privileges. 

Life Members shall pay, on admission, the sum of Ten Pounds. They 
shall receive gratuitously the Reports of the Association which may be 
published after the date of such payment. They are eligible to all the 
offices of the Association. 

Annual Subscribers shall pay, on admission, the sum of Two Pounds, 
and in each following year the sum of One Pound. They shall receive 
gratuitously the Reports of the Association for the year of their admission 
and for the years in which they continue to pay without intermission their 
Annual Subscription. By omitting to pay this subscription in any par- 
ticular year, Members of this class (Annual Subscribers) Insp for that and 



iXVlU RULES OF THE ASSOCIATION. 

all future years tlie privilege of receiving the volumes of the Association 
gratis : but they may resume their Membership and other privileges at 
any subsequent Meeting of the Association, paying on each such occasion 
the sum of One Pound. They are eligible to all the Offices of the Asso- 
•ciation. 

Associates for the year shall pay on admission the sum of One Pound. 
They shall not receive gratuitously the Reports of the Association, nor be 
eligible to serve on Committees, or to hold any office. 

The Association consists of the following classes : — 

1. Life Members admitted from 1831 to 1845 inclusive, who have paid 
on admission Five Pounds as a composition. 

2. Life Members who in 1846, or in subsequent years, have paid on 
admission Ten Pounds as a composition. 

3. Annual Members admitted from 1831 to 1839 inclusive, subject to 
the payment of One Pound annually. [May resume their Membership 
after intermission of Annual Payment.] 

4. Annual Members admitted in any year since 1839, subject to the 
payment of Two Pounds for the first year, and One Pound in each 
ifollowing year. [May resume their Membership after intermission of 
Annual Payment.] 

5. Associates for the year, subject to the payment of One Pound. 

6. Corresponding Members nominated by the Council. 

And the Members and Associates will be entitled to receive the annual 
volume of Reports, gratis, or to 2^^^'''<^^>(^-^^ it at reduced (or Members') 
•price, according to the following specification, viz. : — 

1. Gratis. — Old Life Members who have paid Five Pounds as a com- 

position for Annual Payments, and previous to 1845 a fur- 
ther sum of Two Pounds as a Book Subscription, or, since 
1845, a further sum of Five Pounds, 

New Life Members who have paid Ten Pounds as a compo- 
sition. 

Annual Members who have not intermitted their Annual Sub- 
scription. 

2. At reduced or Memhers" Prices, viz. two-thirds of the Publi- 

cation Price. — Old Life Members who have paid Five Pounds 
as a composition for Annual Payments, but no further sum 
as a Book Subscription. 

Annual Members who have intermitted their Annual Sub- 
scription. 

Associates for the year. [Privilege confined to the volume 
for that year only.] 

3. Members may purchase (for the purpose of completing their sets) 

any of the volumes of the Reports of the Association up 
to 1874, of lohich more than 15 copies remain, at 2s. 6c?. per 
volume. • 
Application to be made at the Office of the Association, 22 Albemarle 
Sti-eet, London, W. 

Volumes not claimed within two years of the date of publication can 
•only be issued by direction of the Council. 

Subscriptions shall be received by the Treasurer or Secretaries. 

' A few complete sets, 1831 to 1874, are on sale, £10 the set. 



RULES OF THE ASSOCIATION. XXIX 

Meetings. 

The Association shall meet annually, for one week, or longer. The- 
place of each Meeting shall be appointed bj^ the General Committee two 
years in advance ; and the arrangements for it shall be entrusted to the 
Officers of the Association. 

General Committee. 

The General Committee shall sit during the week of the Meeting, or 
longer, to transact the business of the Association. It shall consist of the 
following persons : — 

Class A. Peejiaxent Members. 

1. Members of the Council, Presidents of the Association, and Presi- 
dents of Sections for the present and preceding years, with Authors of 
Reports in the Transactions of the Association. 

2. Members who by the publication of Works or Papers have fur- 
thered the advancement of those subjects which are taken into considei-a- 
tion at the Sectional Meetings of the Association. With a view of sub- 
mitting neio claims under this Rule to the decision of the Council, they must 
be sent to the Secretary at least one month before the Meeting of the 
Association. The decision of the Council on the claims of any Member of 
the Association to be placed on the list of the General Committee to be final. 

Class B. Temporary Members.' 

1. Delegates nominated by the Corresponding Societies under the 
conditions hereinafter explained. Claims under this Rule to be sent to the 
Secretary before the opening of the Meeting. 

2. Office-bearers for the time being, or delegates, altogether not ex- 
ceeding three, from Scientific Institutions established in the place of 
Meeting. Claims under this Rule to be approved by the Local Secretaries 
before the opening of the Meeting. 

3. Foreigners and other individuals whose assistance is desired, and 
who are specially nominated in writing, for the Meeting of the year, by 
the President and General Secretaries. 

4. Vice-Presidents and Secretaries of Sections. 

Organizing Sectional Committees.^ 

The Presidents, Vice-Presidents, and Secretaries of the several Sec- 
tions are nominated by the Council, and have power to act until their 
names are submitted to the General Committee for election. 

From the time of their nomination they constitute Organizing Com- 
mittees for the purpose of obtaining information upon the Memoirs and 
Reports likely to be submitted to the Sections,^ and of preparing Reports 
thereon, and on the order in which it is desirable that they should be 
read, to be presented to the Committees of the Sections at their first 

' Revised by the General Committee, 188i. 

- Passed by the General Committee, Edinburgh, 1871. 

' Kofict' to Contribtitoi-s of Memoirs. — Authors are reminded that, under an 
arrangement dating from 1871, the acceptance of Memoirs, and tlie days on which 
they are to be read, are now as far as possible determined by Organizing Committees 
for the several Sections before the hef/inninr/ of the Meeting. It has therefore become 
necessary, in order to give an opportunity to the Committees of doing justice to the 
several Communications, that each Author should prepare an Abstraci'of his Memoir, 
of a length suitable for insertion in tJie published Transactions of the Association, 
and that he should send it, together with the original Memoir, by book-post, on or 



XXX RULES OF THE ASSOCIATION. 

meeting. The Sectional Presidents of former years are ex ojjicio members 
of the Organizing Sectional Committees.' 

An Organizing Committee may also hold such preliminary meetings as 
the President of the Committee thinks expedient, but shall, under any 
circumstances, meet on the first Wednesday of the Annual Meeting, at 
11 A.M., to nominate the first members of the Sectional Committee, if 
they shall consider it expedient to do so, and to settle the terms of their 
report to the General Committee, after -which their functions as an 
Organizing Committee shall cease. ^ 

Constitution of the Sectional Comviittees.^ 

On the first day of the Annual Meeting, the President, Vice-Presi- 
dents, and Secretaries of each Section having been appointed by the 
General Committee, these Officers, and those previous Presidents and 
Vice-Presidents of the Section who may desire to attend, are to meet, at 
2 P.M., in their Committee Rooms, and enlarge the Sectional Committees 
by selecting individuals from among the Members (not Associates) present 
at the Meeting whose assistance they may particularly desire. The Sec- 
tional Committees thus constituted shall have power to add to their 
number from day to day. 

The List thus formed is to be entered daily in the Sectional Minute- 
Book, and a copy forwarded without delay to the Printei-, who is charged 
with publishing the same before 8 A.M. on the next day in the Journal of 
the Sectional Proceedings. 

Business of the Sectional Comviittees. 

Committee Meetings are to be held on the Wednesday at 2 p.m., on the 
following Thursday, Friday, Saturday,^ Monday, and Tuesday, from 10 to 
11 A.M., punctually, for the objects stated in the Rules of the Association, 
and specified below. 

The business is to be conducted in the following manner : — 

1. The President shall call on the Secretary to read the minutes of 

the previous Meeting of the Committee. 

2. No paper shall be read until it has been formally accepted by the 

Committee of the Section, and entered on the minutes accord- 
ingly. 

3. Papers which have been reported on unfavourably by the Organiz- 

ing Committees shall not be brought before the Sectional 
Committees.® 
At the first meeting, one of the Secretaries will read the Minutes of 
last year's proceedings, as recorded in the Minute-Book, and the Synopsis 

before , addressed thus — 'General Secretaries, British Associa- 
tion, 22 Albemarle Street, London, W. For Section ' If it should be incon- 
venient to the Author that his paper should be read on any particular days, he is 
requested to send information thereof to the Secretaries in a separate note. Authors 
who send in their MSS. three complete weeks before the Meeting, and whose papers 
are accepted, will be furnished, before the Meeting, with printed copies of their 
Eeports and Abstracts. No Report, Paper, or Abstract can be inserted in the Annual 
Volume unless it is handed either to the Recorder of the Section or to the Secretary, 
■be/ore the conclusion of the Mcetin/f. 

' Added by the General Committee, Sheffield, 1879. 

2 Revised by the General Committee, Swansea, 1880. 

' Passed by the General Committee, Edinburgh, 1871. 

* The meeting on Saturday was made optional by the General Committee at 
Pouthport, 1883. 

' These rules were adopted by the General Committee, Plymouth, 1877. 



KOLES OF THE ASSOCIATION. XXXI 

of Recommendatious adopted at the last Meeting of the Association and 
printed in the last volume of the Transactions. He will next proceed to 
read the Report of the Organizing Committee.' The list of Communi- 
cations to be read on Thursday shall be then arranged, and the general 
distribution of business throughout the week shall be provisionally ap- 
pointed. At the close of the Committee Meeting the Secretaries shall 
forward to the Printer a List of the Papers appointed to be read. The 
Printer is charged vidth publishing the same before 8 A.M. on Thursday in 
the Journal. 

On the second day of the Annual Meeting, and the follovring days, 
the Secretaries are to correct, on a copy of the Joui-nal, the list of papers 
which have been read on that day, to add to it a list of those appointed 
to be read on the next day, and to send this copy of the Journal as early 
in the day as possible to the Printer, who is charged with printing the 
same before 8 a.m. next morning in the Journal. It is necessary that one 
of the Secretaries of each Section (generally the Recorder) should call 
at the Printing Office and revise the proof each evening. 

Minutes of the proceedings of every Committee are to be entered daily 
in the Minute-Book, which should be confirmed at the next meeting of 
the Committee. 

Lists of the Reports and Memoirs read in the Sections are to be entered 
in the ^linute-Book daily, which, with all Memoirs and Copies 07- Abstracts 
of Memoirs furnished hy Autlwrs, are to hefonvarded, at the close of the Sec- 
tional Meetings, to the Secretary. 

The Vice-Presidents and Secretaries of Sections become ex officio tem- 
porary Members of the General Committee (vide'p. xxix), and will receive 
on application to the Treasurer in the Reception Room, Tickets entitling 
them to attend its Meetings. 

The Committees will take into consideration any suggestions which may 
be offered by their Members for the advancement of Science. They are 
specially requested to review the recommendations adopted at preceding 
Meetings, as published in the volumes of the Association and the com- 
munications made to the Sections at this Meeting, for the purposes of 
selecting definite points of research to which individual or combined 
exertion may be usefully directed, and branches of knowledge on the state 
and progress of which Reports are wanted ; to name individuals or Com- 
mittees for the execution of such Reports or researches ; and to state 
whether, and to what degree, these objects may be usefully advanced by 
+he appropriation of the funds of the Association, by application to 
Government, Philosophical Institutions, or Local Authorities. 

In case of appointment of Committees for special objects of Science 
it is expedient that all Members of the Committee shovld be named and 
one of them appointed to act as Secretary, for insuring attention to business. 

Committees have power to add to their number persons whose assist- 
ance they may require. 

The recommendations adopted by the Committees of Sections are to 
be registered in the Forms furnished to their Secretaries, and one Copy of 
each is to be forwarded, without delay, to the Secretary for presentation 
to the Committee of Recommendations. Unless this be done, the Eecom- 
mendations cannot receive the sanction of the Association. 

N.B. — Recommendations which may originate in any one of the Sec- 
tions must first be sanctioned by the Committee of that Section before they 

' This and the following sentence were added by the General Committee 1871. 



xxxii KULES OF THE ASSOCIATION. 

can be referred to the Committee of Recommendations or confirmed by 
the General Committee. 

The Committees of the Sections shall ascertain whether a Report has 
been made by every Committee appointed at the previous Meeting to whom 
a sum of money has been granted, and shall report to the Committee of 
Recommendations in every case where no such Report has been received.' 

Notices regarding Ghxmts of Money. 

Committees and individuals, to whom grants of money have been 
entrusted by the Association for the prosecution of particular researches 
in science, are required to present to each following Meeting of the 
Association a Report of the progress which has been made ; and the 
Individual or the Member first named of a Committee to whom a money 
grant has been made must (previously to the next Meeting of the Associa- 
tion) forward to the General Secretaries or Treasurer a statement of the 
sums which have been expended, and the balance which remains dispos- 
able on each grant. 

Grants of money sanctioned at any one Meeting of the Association 
expire a lueek before the opening of the ensuing Meeting: nor is the 
Treasurer authorized, after that date, to allow any claims on account of 
such grants, unless they be renewed in the original or a modified form by 
the General Committee. 

No Committee shall raise money in the name or under the auspices of 
the British Association without special permission from the General Com- 
mittee to do so ; and no money so raised shall be expended except in 
accordance with the rules of the Association. 

In each Committee, the Member first named is the only person entitled 
to call on the Treasurer, Professor A. W. Williamson, University College, 
London, W.C, for such portion of the sums granted as may from time to 
time be required. 

In grants of money to Committees, the Association does not contem- 
plate the payment of personal expenses to the members. 

In all cases where additional grants of money are made for the con- 
tinuation of Researches at the cost of the Association, the sum named is 
deemed to include, as a part of the amount, whatever balance may remain 
unpaid on the former grant for the same object. 

All Instruments, Papei-s, Drawings, and other property of the Associa- 
tion are to be deposited at the OfiBlce of the Association, 22 Albemarle 
Street, Piccadilly, London, W., when not employed in carrying on scien- 
tific inquiries for the Association. 

Business of the Sections. 

The Meeting Room of each Section is opened for conversation from 
10 to 11 daily. The Section Booms and approaches thereto can he used for 
no notices, exhibitions, or other purposes than those of the Association. 

At 11 precisely the Chair will be taken, ^ and the reading of communi- 
cations, in the order previously made public, commenced. At 3 p.m. the 
Sections will close. 

Sections may, by the desire of the Committees, divide them.3elves into 
Departments, as often as the number and nature of the communications 
delivered in may render such divisions desirable. 

' Passed by the General Committee at Sheffield, 1879. 

- The meeting on Saturday may begin, if desired by the Committee, at any time not 
earlier than 10 or later than 11. Passed by the General Committee at Southport, 188.3. 



RULES OF THE ASSOCIATION. XXXm 

A Report presented to the Association, and read to the Section which 
originally called for it, may be read in another Section, at the request of 
the Officers of that Section, with the consent of the Author. 

Duties of the Doorkeepers. 

1. — To remain constantly at the Doors of the Rooms to which they are 
appointed during the whole time for which they are engaged. 

2. — To require of every person desirous of entering the Rooms the ex- 
hibition of a Member's, Associate's, or Lady's Ticket, or Reporter's 
Ticket, signed by the Treasurer, or a Special Ticket signed by the 
Secretary. 

3. — Persons unprovided with any of these Tickets can only be admitted 
to any particular Room by order of the Secretary in that Room. 
No person is exempt from these Rules, except those Officers of the 

Association whose names are printed in the programme, p. 1. 

Duties of the Messengers. 
To remain constantly at the Rooms to which they are appointed dar- 
ing the whole time for which they are engaged, except when employed on 
messages by one of the Officers directing these Rooms. 

Committee of Recommendations. 

The General Committee shall appoint at each Meeting a Committee, 
which shall receive and consider the Recommendations of the Sectional 
Committees, and report to the Geneml Committee the measures which 
they would advise to be adopted for the advancement of Science. 

All Recommendations of Grants of Money, Requests for Special Re- 
searches, and Reports on Scientific Subjects shall be submitted to the 
Committee of Recommendations, and not taken into consideration by the 
General Committee unless previously recommended by the Committee of 
Recommendations. 

Ooo'responding Societies.^ 

(1.) Any Society is eligible to be placed on the List of Corresponding 
Societies of the Association which undertakes local scientific investiga- 
tions, and publishes notices of the results. 

(2.) Applications may be made by any Society to be placed on the 
List of Corresponding Societies. Application must be addressed to the 
Secretary on or before the 1st of June preceding the Annual Meeting at 
which it is intended they should be considered, and must be accompanied 
by specimens of the publications of the results of the local scientific 
investigations recently undertaken by the Society. 

(3.) A Corresponding Societies Committee shall be annually nomi- 
nated by the Council and appointed by the General Committee for the 
purpose of considering these applications, as well as for that of keeping 
themselves generally informed of the annual work of the Corresponding 
Societies, and of superintending the preparation of a list of the papers 
published by them. This Committee shall make an annual report to the 
General Committee, and shall suggest such additions or changes in the 
List of Corresponding Societies as they may think desirable. 

(4.) Every Corresponding Society shall return each year, on or 
before the 1st of June, to the Secretary of the Association, a schedule, 
' Pas.serl by the General Committee, 1884. 

1885. b 



-XXXiv RULES OP THE ASSOCIATION. 

properly filled np, which will be issued by the Secretary of the Associa- 
tion, and which will contain a request for such particulars with regard to 
the Society as may be required for the information of the Corresponding 
Societies Committee. 

(5.) There shall be inserted in the Annual Report of the Association 
a list, in an abbreviated form, of the papers published by the Corre- 
sponding Societies during the past twelve months which contain the 
results of the local scientific work conducted by them ; those papers only 
Taeing included which refer to subjects coming under the cognizance of 
one or other of the various Sections of the Association. 

(0.) A Corresponding Society shall have the right to nominate any 
one of its members, who is also a Member of the Association, as its dele- 
gate to the Annual Meeting of the Association, who shall be for the time 
a Member of the General Committee. 

Conference of Delegates of Corresponding Societies. 

(7.) The Delegates of the various Corresponding Societies shall con- 
stitute a Conference, of which the Chairman, Vice- Chairmen, and Secre- 
taries shall be annually nominated by the Council, and appointed by the 
General Committee, and of which the members of the Coi-responding 
Societies Committee shall be ex officio members. 

(8.) The Conference of Delegates shall be summoned by the Secretaries 
to hold one or more meetings during each Annual Meeting of the Associa- 
tion, and shall be empowered to invite any Member or Associate to take 
part in the meetings. 

(9.) The Secretaries of each Section shall be instructed to transmit to 
the Secretaries of the Conference of Delegates copies of any recommenda- 
tions forwarded by the Presidents of Sections to the Committee of Re- 
commendations bearing upon matters in which the co-operation of 
Corresponding Societies is desired ; and the Secretaries of the Conference 
of Delegates shall invite the authors of these recommendations to attend 
the meetings of the Conference and give verbal explanations of their 
objects and of the precise way in which they would desire to have them 
carried into efiect. 

(10.) It will be the duty of the Delegates to make themselves familiar 
with the purport of the several recommendations brought before the Confer- 
ence, in order that they and others who take part in the meetings may be 
able to bring those recommendations clearly and favourably before their 
respective Societies!. The Conference may also discuss propositions bear- 
ing on the promotion of more systematic observation and plans of opera- 
tion, and of greater uniformity in the mode of publishing I'esults. 

Local Cornmittees. 

Local Committees shall be formed by the Officers of the Association 
to assist in making arrangements for the Meetings. 

Local Committees shall have the power of adding to their numbers 
those Members of the Association whose assistance they may desire. 

Officers. 

A President, two or more Vice-Presidents, one or more Secretaries, 
and a Treasurer shall be annually appointed by the General Committee. 



RULES OF THE ASSOCIATION. XXXV 

Council. 

In the intervals of the Meetings, the affairs of the Association shall 
be managed by a Conncil appointed by the General Committee. The 
Council may also assemble for the despatch of business during the week 
of the Meeting. 

Papers and Communications. 

The Author of any paper or communication shall be at liberty to 
reserve his right of property therein. 

Accounts. 

The Accounts of the Association shall be audited annually, by Auditors 
appointed by the General Committee. 



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PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



xliii 



Presidents and Secretaries of the Sections of the Association. 



Date and Place 



Presidents 



Secretaries 



MATHEMATICAL AND PHYSICAL SCIENCES. 

COMMITTEE OF SCIENCES, I. — MATHEMATICS AND GENERAL PHYSICS. 



1832. Oxford 

1833. Cambridge 



Davies Gilbert, D.C.L., F.E.S. 
Sir D. Brewster, F.R.S. 



1834. Edinburgh Rev. W. ^Vhewell, F.R.S. 



Rev. H. Coddington. 

Prof. Forbes. 

Prof. Forbes, Prof. Lloyd. 



1835. Dublin 

1836. Bristol 

1837. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Plymouth 

1842. Manchester 



SECTION A. — MATHEMATICS AND PHYSICS. 
Rev. Dr. Robinson 



1843. Cork 

1844. York 

1845. Cambridge 

1846. Southamp- 
ton. 

1847. Oxford 



1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 

1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 



1858. Leeds 



Rev. William WTiewell, F.R.S. 

Sir D. Brewster, F.R.S 

Sir J. F. W. Herschel, Bart., 

F.R.S. 
Rev. Prof . Whewell, F.R.S.... 

Prof. Forbes, F.R.S 

Rev. Prof. Lloyd, F.R.S 

Very Rev. G. Peacock, D.D., 

F R S 
Prof. M'Culloch, M.R.I. A. ... 
The Earl of Rosse, F.R.S. ... 
The Very Rev. the Dean of 

Ely. 
Sir John F. W. Herschel, 

Bart., F.R.S. 
Rev. Prof. Powell, M.A., 

F.R.S. 

Lord Wrottesley, F.R.S 

William Hopkins, F.R.S 

Prof. J. D. Forbes, F.E.S., 

Sec. R.S.E. 
Rev. W. Whewell, D.D., 

F.R.S. 
Prof. W. Thomson, M.A., 

F.R.S. L. & E. 
The Verj' Rev. the Dean of 

Ely, F.R.S. 
Prof. G. G. Stokes, M.A., Sec. 

E.S. 
Rev. Prof. Kelland, M.A., 

F.R.S. L. & E. 
Rev. R. Walker, M.A., F.R.S. 

Rev. T. R. Robinson, D.D., 
F.R.S., M.R.I.A. 

Rev. W. Whewell, D.D., 
V.P.R.S. 



Prof. Sir W. R. Hamilton, Prof. 

Wheatstone. 
Prof. Forbes, W. S. Harris, F. W. 

Jerrard. 
W. S. Harris, Rev. Prof. Powell, 

Prof. Stevelly. 
Rev. Prof. Chevallier, Major Sabine, 

Prof. Stevelly. 
J. D. Chance, W. Snow Harris, Prof. 

Stevelly. 
Rev. Dr. Forbes, Prof. Stevelly, 

Arch. Smith. 
Prof. Stevelly. 
Prof. M'Cuhoch, Prof. Stevelly, Rev. 

W. Scoresby. 
J. Nott, Prof .■ Stevelly. 
Rev. Wm. Hey, Prof. Stevelly. 
Rev. H. Goodwin, Prof. Stevelly, 

G. 6. Stokes. 
John Drew, Dr. Stevelly, G. G. 

Stokes. 
Rev. H. Price, Prof. Stevelly, G. G. 

Stokes. 
Dr. Stevelly, G. G. Stokes. 
Prof. Stevelly, G. G. Stokes, W. 

Eidout Wills. 
W. J.Macquorn Rankine, Prof .Smyth, 

Prof. Stevelly, Prof. G. G. Stokes. 
S. Jackson, W. J. Macquorn Rankine, 

Prof. Stevelly, Prof. G. G. Stokes. 
Prof. Dixon, W. J. Blacquorn Ran- 
kine, Prof. Stevelly, J. Tyndall. 

B. Blaydes Haworth, J. D. Sollitt, 
Prof. Stevelly, J. Welsh. 

J. Hartnup, H. G. Puckle, Prof. 

Stevelly, J. Tyndall, J. Welsh. 
Rev. Dr. Forbes, Prof. D.Gray, Prof. 

Tyndall. 

C. Brooke, Rev. T. A. Southwood, 
Prof. Stevelly, Rev. J. C. Turnbull. 

Prof. Curtis, Prof. Hennessy, P. A. 

Ninnis, W. J. Macquorn Rankine, 

Prof. Stevelly. 
Rev. S. Earnshaw, J. P. Hennessy, 

Prof. Stevelly, H.J. S.Smith, Prof. 

Tyndall. 



xliv 



REPORT — 1885. 



Date and Place 



1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton... 

1873. Bradford... 

1874. Belfast 

1875. Bristol 

1876. Glasgow ... 

1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 

1880. Swansea ... 

1881. York 

1882. Southamp- 

ton. 

1883. Southport 

1884. Montreal ... 

1885. Aberdeen... 



Presidents 



The Earl of Kosse, M.A., K.P., 
Rev. B. Price, M.A., F.E.S.... 

G. B. Airy, M.A., D.C.L., 

F.R.S. 
Prof. G. G. Stokes, M.A., 

F.R.S. 
Prof . W. J. Macquorn Rankine, 

C.E., F.R.S. 
Prof. Cayley, M.A., F.R.S., 

F.B.A.S. 
W. Spottiswoode,M.A.,F.R.S., 

F.R.A.S. 

Prof. Wheatstone, D.C.L., 

F.R.S. 
Prof. Sir W. Thomson, D.C.L., 

F.R.S. 
Prof. J. Tyndall, LL.D., 

F.R.S. 
Prof. J. J. Sylvester, LL.D., 

F.R.S. 
.J. Clerk Maxwell, M.A., 

LL.D., F.R.S. 

Prof. P. G. Tait, F.R.S.E. ... 



VV. De La Rue, D.C.L., F.R.S. 

Prof. H. J. S. Smith, F.R.S. 

Rev. Prof. J. H. Jellett, M.A.. 
M.R.I.A. 

Prof. Balfour Stewart, M.A., 

LL.D., F.R.S. 
Prof. Sir W. Thomson, M.A., 

D.C.L., F.R.S. 

Prof. G. C. Foster, B.A., F.R.S., 

Pres. Physical Soc. 
Rev. Prof. Salmon, D.D., 

D.C.L., F.R.S. 
Geortce Johnstone Stoney, 

M.A., F.R.S. 
Prof. W. Grylls Adams, M.A., 

F.R.S. 
Prof. Sir W. Thomson, M.A., 

LL.D., D.C.L., F.R.S. 
Rt. Hon. Prof. Lord Rayleigh, 

M.A., F.R.S. 
L'rof . 0. Heurici, Ph.D.,F.R.S., 

Prof. Sir W. Thomson, M.A., 
LL.D., D.C.L., F.R.S 

Prof. G. Chrystal, M.A., 
F.R.S.E. 



Secretaries 



J. P. Hennessy, Prof. Maxwell, H. 

J. S. Smith, Prof. Stevelly. 
Rev. G. C. Bell, Rev. T. Rennison, 

Prof. Stevelly. 
Prof. R. B. Clifton, Prof. H. J. S. 

Smith, Prof. Stevelly. 
Prof. R. B. Clifton, Prof. H. J. S. 

Smith, Prof. Stevelly. 
Rev.N.Ferrers,Prof.Fuller,F.Jenkin, 

Prof. Stevellv, Rev. C. T. Wiitley. 
Prof. Fuller, F. Jenkin, Rev. G. 

Buckle, Prof. Stevelly. 
Rev. T. N. Hutchinson, V. Jenkin, G. 

S. Mathews, Prof. H. J. S. Smith, 

J. M. Wilson. 
Fleeming Jenkin, Prof. H. J.S.Smith, 

Rev. S. N. Swann. 
Rev. G. Buckle, Prof. G. C. Foster, 

Prof. Fuller, Prof. Swan. 
Prof. G. C. Foster, Rev. R. Harley, 

R. B. Havward. 
Prof. G. C. Foster, R. B. Hay ward, 

W. K. Clifford. 
Prof. W. G. Adams, W. K. Clifford, 

Prof. G. C. Foster, Rev. W. Allen 

Whit worth. 
Prof. W. G. Adams, J. T. Bottomlev, 

Prof. W. K. Clifford, Prof. J. I). 

Everett, Rev. R. Harle)'. 
Prof. W.K. Clifford, .LW.L.Glaisher, 

Prof . A. S. Herschel, G. F. Rodwell. 
Prof. W. K. Clifford, Prof. Forbes, J. 

W.L. Glaisher, Prof. A. S. Herschel. 
J. W. L. Glai.sher, Prof. Herschel, 

Randal Nixon, J. Perry, G. F. 

Rodwell. 
Prof. W. F. Barrett, J. W.L. Glaisher, 

C. T. Hudson, G. F. Rodwell. 
Prof. W. F. liarrett, J. T. Bottomley, 

Prof. G. Forbes, J. W. L. Glaisher, 

T. Muir. 
Prof. W. F. Barrett, J. T. Bottomley, 

J. W. L. Glaisher, F. G. Landon. 
Prof. J. Casey, G. F. Fitzgerald, J. 

W. L. Glaisher, Dr. O. J. Lodge. 
A. H. Allen, J. W. L. Glaisher,''Dr. 

O. J. Lodge, D. MacAlister. 
W. E. Ayrtion, J. W. L. Glaisher, 

Dr. O. J. Lodge, D. MacAlister. 
Prof. W. E. Ayrton, Prof. O. J. Lodge, 

D. IMacAlister, Rev. W. Routh. 
W. M. Hicks, Prof. O. J. Lodge, 

D. MacAlister, Rev. G. Richardson. 
W. M. Hicks, Prof. O. J. Lodge, 

D. ilacAlister, Prof. R. C. Rowe. 
C. Carpmael, W. M. Hicks, Prof. A. 

Johnson, Prof. O. J. Lodge, Dr. D. 

MncAlister. 
R. E. Baynes, R. T. Glazebroob, Prof. 

W. M. Hicks, Prof. W. Ingram. 



TBESIDENTS AND SECRETAEIES OF THE SECTIONS. 



xlv 



CHEMICAL SCIENCE. 

COMMITTEE OF SCIENCES, II. — CHEMTSTRT, MINERALOGY. 



Date and Place 



Presidents 



1832. 
18.33. 
1834. 



183.5. 
1836. 

1837. 

1838. 

1839. 
1840. 



Oxford 

Cambridge 
Edinburuh 



■John Dalton, D.C.L., F.R.S. 

; John Dalton, D.C.L., F.R.S. 

Dr. Hope 



Secretaries 



James F. W. Johnston. 

Prof. Miller. 

Mr. Johnston, Dr Christison. 



Dublin . 
Bristol . 



Liverpool... 

Newcastle 

Birmingham 
Glasgow ... 



1841. Plymouth... 



1842. 
1843. 
1844. 
1845. 

1846, 

1847. 

1848. 
1849. 
1850. 
1851. 
1852. 



Manchester 

Cork 

York 

Cambridge 

Soiithamp- 

ton 
Oxford 



SECTION B, — CHEMISTRY AND MINERALOGY. 

Dr. T. Thomson, F.R.S IDr. Apjohn, Prof. Johnston. 

Rev. Prof. Gumming Dr. Apjohn, Dr. C.Henry, \V. Hera- 
path. 

Prof. Johnston, Prof. Miller, Dr. 
Reynolds. 

Prof. Miller, H. L. Pattinson, Thomas 
Richardson. 

Dr. Golding Bird, Dr. J. B. Melson. 

Dr. R. D/Thomson, Dr. T. Clark, 
Dr. L. Playfair. 

J. Prideaux, Robert Hunt, W. M. 
Tweedy. 

Dr. L. Playfair, R. Hunt, J. Graham. 

R. Hunt, Dr. Sweeny. 

Dr. I.. Playfair, E. Solly, T. H. Barker. 

R. Hunt, J. P. Joule, Prof. Miller, 
E. Solly. 

Dr. Miller, R. Hunt, W. Randall. 



Swansea ... 
Birmingham 
Edinburgh 
Ipswich . . . 
Belfast 



1853. Hull 



1854. 
1855. 
1856. 

1857. 

1858. 

1859. 

1860. 

1861, 
1862. 



Liverpool 
Glasgow .,. 
Cheltenham 

Dublin 

Leeds 

Aberdeen... 

Oxford 



Manchester 
Cambridge 



1863. Newcastle 



1864. 
1865. 



Bath 

Birmingham 



Michael Faraday, F.R.S 

Rev. William Whewell,F.R.S. 

Prof. T. Graham, F.R.S 

Dr. Thomas Thomson, F.R.S. 

Dr. Daubeny, F.R.S 

John Dalton, D.C.L., F.R.S. 

Prof. Apjohn, M.R.LA 

Prof. T. Graham, F.R.S 

Rev. Prof. Gumming 



Michael Faraday, D.C.L., 

F.R.S. 
Rev. W. V. Harcourt, M.A., 

F.R.S. 

Richard Phillips, F.R.S 

John Perc3% M.D., F.R.S 

Dr. Christison, V.P.R.S.B. 
Prof. Thomas Graham, F.R.S. 
Thomas Andrews,M.D., F.R.S. 

Prof. J. F. W. Johnston, M.A., 

F.R.S. 
Prof.W. A.Miller, M.D.,F.R.S. 
Dr. Lyon Playfair.C.B., F.R.S. 
Prof. B. C. Brodie, F.R.S. ... 

Prof. Apjohn, M.D., F.R.S., 

M.R.LA. 
Sir J. F. W. Herschel, Bart., 

D.C.L. 
Dr. Lyon Playfair, C.B., F.R.S. 

Prof.B. C. Brodie, F.R.S 

Prof. W.A.Miller, M.D.,F.R.S. 
Prof. W.A.Miller, M.D.,F.R.S. 

Dr. Alex. W. Williamson, 

F.R.S. 
W.Odling, M.B.,F.R.S.,F.C.S. 
Prof. W. A. Miller, M.D., 

Y.P.R.S. 



B. G. Brodie, R. Hunt, Prof. Solly. 

T. H. Henry, R. Hunt, T. AVilliams. 

R. Hunt, G. Shaw. 

Dr. Anderson, R. Hunt, Dr. Wilson. 

T. J. Pearsall, W. S. Ward. 

Dr. Gladstone, Prof. Hodges, Prof. 
Ronalds. 

H. S. Blimdell, Prof. R. Hunt, T. J. 
Pearsall. 

Dr.Ed wards, Dr. Gladstone, Dr.Price. 

Prof. Frankland, D)-. H. E. Roscoe. 

J. Horsley, P. J. Worsley, Prof. 
Voelcker. 

Dr. Davy, Dr. Gladstone, Prof. Sul- 
livan. 

Dr. Gladstone, W. Odling, R. Rey- 
nolds. 

J. S. Brazier, Dr. Gladstone, G. D. 
Liveing, Dr. Odling. 

A. Vernon Harcourt, G. D. Liveing, 
A. B. Northcote. 

A. Vernon Harcourt, G. D. Liveinc. 

H. W. Elphinstone, W. Odling, Prof. 
Roscoe. 

Prof. Liveing, H. L. Pattinson, J. C. 
Stevenson. 

A.V.Harcourt,Prof.Liveing,R.Biggs. 

A. V. Harcourt, H. Adkiris, Prol. 
Wanklyn, A. Winkler Wills. 



xlvi 



EEPOKT 1885. 



Date and Place 



1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton.. 

1873. Bradford.. 

1874. Belfast 

1875. Bristol 

1876. Glasgow .. 

1877. Plymouth.. 

1878. Dublin 

1879. Sbeffield .. 

1880. Swansea .. 



Presidents 



Secretaries 



H. Bence Jones, M.D.,F.E.S. 



1881. York. 



1882. Southamp 
ton 



Prof. H. E. Roscoe, B.A., 

F.R.S., F.C.S. 
Prof. T. Andrews, M.D.,F.R.S. 



J. H. Atherton, Prof. Liveing, W. J. 
Russell, J. White. 
Prof. T. Anderson, M.D., A. Crum Brown, Prof. G. D. Liveing, 

F.R.S.E. i W. J. Russell. 

Prof. E. Frankland, F.R.S., Dr. A. Crum Brown, Dr. W. J. Rus- 

F.C.S. sell, F. Sutton. 

Dr. H. Debus, F.R.S., F.C.S. Prof. A. Crum Brown, Dr. W. J. 

Russell, Dr. Atkinson. 
Prof. A. Crum Brown. A. E. Fletcher, 

Dr. W. J. Russell. 
J. T. Buchanan, W. N. Hartley, T. 
E. Thorpe. 
Dr. J. H. Gladstone, F.R.S.... Dr. Mills, W. Chandler Roberts, Dr. 

! W. J. Russell, Dr. T. Wood. 
Prof. W. J. Russell, F.R.S.... , Dr. Armstrong, Dr. Mills, W. Chand- 

J ler Roberts, Dr. Thorpe. 
Prof. A. Crum Brown, M.D., Dr. T. Cranstoun Charles, W. Chand- 

F.R.S.E., F.C.S. I ler Roberts, Prof. Thorpe. 

A. G. Vernon Harcourt, M.A., Dr. H. E. Armstrong, W. Chandler 
F.R.S., F.C.S. 1 Roberts, W. A. Tilden. 

W. H. Perkin, F.R.S W. Dittmar, W. Chandler Roberts, 

J. M. Thomson, W. A. Tilden. 
F. A. Abel, F.R.S., F.C.S. ... Dr. Oxland. W. Cliandler Roberts, 

I J. M. Thomson. 
Prof. Maxwell Simpson, M.D.,'W. Chandler Roberts, J. M. Thom- 
F.R.S., F.C.S. I son. Dr. C. R. Tichborne, T. Wills. 

Prof. Dewar, M.A., F.R.S. IH. S. Bell, W. Chandler Roberts, J. 

M. Thomson. 
Joseph Henry Gilbert, Ph.D.,' H. B. Dixon, Dr. W. R. Eaton Hodg- 
F.R.S. kinson, P. Phillips Bedson, J. M. 

Thomson. 
Prof. A. W.Williamson, Ph.D., P. Phillips Bedson, H. B. Dixon, 

F.R.S. 1 T. Gough. 

Prof. G. D. Liveing, M.A., P. Phillips Bedson, H. B. Dixon, 
F.R.S. I J. L. Notter. 

1883. Southport Dr. J. H. Gladstone, F.R.S... I Prof. P. Phillips Bedson, H. B. 

' ! Dixon, H. Forster Morley. 

1884. Montreal ... Prof. Sir H. E. Roscoe, Ph.D., Prof. P. Phillips Bedson, H.B. Dixon, 

LL.D., F.R.S. T. McFarlane, Prof. W. H. I'ikc. 

188.'5. Aberdeen... Prof. H. E. Armstrong, Ph.D., Prof. P.Phillips Bedson, H. B. Dixon, 
I F.R.S., Sec. C.S. : H. Forster Morley, Dr. W. J. 

I I Simpson. 

GEOLOGICAL (and, until 1851, GEOGRAPHICAL) SCIENCE. 

COMMITTEE OF SCIENCES, III. — GEOLOGY AND GEOGKAPHY. 

1832. Oxford IR. L Murchi.sou, F.R.S ^ John Taylor. 

1833. Cambridge. !g. B. Greenough, F.R.S W. Lonsdale, John Phillips. 

1834. Edinburgh .[Prof. Jameson ! Prof . Phillips, T. Jameson Torrie, 

i Rev. J. Yates. 



1835. Dublin. 

1836. Bristol . 



1837. Liverpool... 



SECTION C. — GEOLOGY AND GEOGKAPHY. 

R. J. Griffith ; Captain Portlock, T. J. Torrie. 

Rev. Dr. Buckland, F.R.S. — William Sanders, S. Stutchbury, 

6^e(>(/>'ff/^7i!y, R. L Murchison, ! T.J. Torrie. 

F.R.S. j 

Rev. Prof. Sedgwick, F.R.S.— ; Captain Portlock, R. Hunter. — Geo- 

Geoffrap7iy,G.'B.GYeenough, fjraphy, Captain H. M. Denham, 

F.R.S. R.N. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



xlvii 



Date and Place 



1838. Newcastle. . 

1839. Birmingham 

1S40. Glasgow ... 

1811. Plymouth... 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge. 

1846. Southamp- 

ton. 

1847. Oxford 

1848. Swansea ... 
1 849.Birmingham 
1850. Edinburgh' 



Presidents 



C. Lyell, F.K.S., V.P.G.S.— 

Geoqraphy, Lord Prudhope. 
Kev. i)r. Buckland, F.R.S.— 

Gcoqraphy, G.B.Greenough, 

F.R.S. 
Charles Lyell, F.R.S.— C'ert- 

graj>hy, G. B. Greenough, 

F.R.S. 
H. T. Dela Beche, F.R.S. ... 

R. I. Mm-chison, F.R.S 

Richard E. Griffith, F.R.S., 
M.R.LA. 

Henry Warbui-ton, M.P.,Pres. 
Geol. Soc. 

Rev. Prof. Sedgwick, M.A., 
F.R.S. 

Leonard Horner,F.R.S. — Geo- 
graphy, G. B. Greenough, 
F.R.S. 

Very Rev.Dr.Buckland,F.R.S. 

Sir H. T. De la Beche, C.B., 

F.R.S. 
Sir Charles Lyell, F.R.S., 

F.G.S. 
Sir Roderick I. Murchison, 

F.R.S. 



Secretaries 



W. C. Trevelyan, Capt. Portlock. — 
Geoqraphy, Capt. Washington. 

George Lloyd, M.D., H. E. Strick- 
land, Charles Darwin. 

W. J. Hamilton, D. Milne, Hugh 
Murray, H. E. Strickland, John 
Scoular, M.D. 

W. J. Hamilton, Edward Moore, M.D., 
R. Hutton. 

E. W. Binney, R. Hutton, Dr. R. 
Lloyd, H. E. Strickland. 

Francis M. Jennings, H. E. Strick- 
land. 

Prof. Ansted, E. H. Bunbury. 

Rev. J. C. Gumming, A. C. Ramsay, 

Rev. W. Thorp. 
Robert A. Austen, Dr. J. H. Norton, 

Prof. Oldham. — Geoyrajjhy, Dr. C. 

T. Beke. 
Prof. Ansted, Prof. Oldham, A. C. 

Ramsay, J. Ruskin. 
Starling Benson, Prof. Oldham, 

Prof. Ramsay. 
J. Beete Jukes, Prof. Oldham, Prof. 

A. C. Ramsay. 
A. Keith Johnston, Hugh Miller, 

Prof. Nicol. 



1851. Ipswich 

1852. Belfast. 



1853. Hull 

1854. Liverpool . . 

1855. Glasgow ... 

1856. Cheltenham 



1857. Dublin 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 



SECTION c (^continued'). — geology. 
WilliamHopkins, M. A.,F.R.S. 



Lieut-Col. Portlock, R.E., 
F.R.S. 

Prof. Sedgwick, F.R.S 

Prof. Edward Forbes, F.R.S. 



Prof. A. C. Ramsay, F.R.S.... 
The Lord Talbot de Malahide 



C. J. F. Bunbuiy, G. W. Ormerod, 

Searles Wood. 
James Bryce, James MacAdam, 

Prof. M'Coy, Prof. Nicol. 
Prof. Harkness, William Lawton. 
John Cunningham, Prof. Harkness, 
G. W. Ormerod, J. W. Woodall. 
Sir R. I. Murchison, F.R.S.... James Bryce, Prof. Harkness, Prof. 

Nicol. 
Rev. P. B. Brodie, Rev. R. Hep- 
worth, Edward Hull, J. Scougall, 
T. Wright. 
Prof. Harkness, Gilbert Sanders, 
Robert H. Scott. 
William Hopkins,M.A.,LL.D., Prof. Nicol, H. C. Sorby, E. W. 

F.R.S. Shaw. 

Sir Charles Lyell, LL.D., Prof. Harkness, Rev. J. Longmuir, 

D.C.L., F.R.S. j H. C. Sorby. 

Rev. Prof. Sedgwick, LL.D.,! Prof. Harkness, Edward Hull, Capt. 

F.R.S., F.G.S. D. C. L. Woodall. 

Sir R. I. Murchison, D.C.L., Prof. Harkness, Edward Hull, T. 

LL.D., F.R.S. Rupert Jones, G. W. Ormerod. 

J. Beete Jukes, M.A., F.R.S. Lucas Barrett, Prof. T. Rupert 

Jones, H. C. Sorby. 

' At a meeting of the General Committee held in 1850, it was resolved ' That 
the subject of Geography be separated from Geology and combined with Ethnology, 
to constitute a separate Section, under the title of the " Geographical and Ethno- 
logical Section," ' for Presidents and Secretaries of which see page lii. 



xlviii 



EEPORT — 1885. 



Date and Place 

1863. Newcastle 

1864. Bath 

1865. Birminghani 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton... 
187.3. Bradford... 

1874. Belfast 

1875. Bristol 

1876. Glasgow .. 

1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 

1880. Swansea ... 

1881. York 

1882. Southamp- 

ton. 

1883. Southport 

1884. Montreal ... 

1885. Aberdeen... 



Presidents 



Secretaries 



Prof. Warington W. Smyth, 

F.R.S., F.G.S, 
Prof. J. Phillips, LL.D., 

F.E.S., F.G.S. 
Sir R. I. MurchisoD, Bart., 

K.C.B. 
Prof. A. C. Ramsay. LL.D., 

F.R.S. 
Archibald Geikie, F.R.S., 

F.G.S. 
R. A. C. Godwin-Austen, 

F.R.S., F.G.S. 
Prof. R. Harkness, F.R.S., 

F.G.S. 
SirPhilipde M.Grey Es^erton, 

Bart., M.P., F.R.S. 
Prof. A. Geikie, F.R.S., F.G.S. 

R. A. C. Godwin-Austen,] 

F.R.S., F.G.S. 
Prof. J. Phillips, D.C.L., 

F.R.S., F.G.S. 
Prof. Hull, M.A., F.R.S., 

F.G.S. 
Dr. Thomas Wright, F.R.S.E., 

F.G.S. 
Prof. John Yoiing, M.D 

W. Pengelly, F.R.S 

.John Evans, D.C.L., F.R.S., 

F.S.A., F.G.S. 
Prof. P. Martin Duncan, M.B., 

F.R.S., F.G.S. 
H. C. Sorby, LL.D., F.R.S., 

F.G.S. 
A. C. Ramsay, LL.D., F.R.S., 

V c ^ 
R. Etheridge, F.R.S., F.G.S. 

Prof. W. C. Williamson, 

LL.D., F.R.S. 
W. T. Blanford, F.R S., Sec. 

G.S. 
Prof. .7. W. Judd, F.R.S., Sec. 

G.S. 



E. F. Boyd, John Daglish, H. C. 
Sorbv, Thomas Sopwith. 

W. B. Dawkins, J. Johnston, H. C. 

Sorbj', W. Pengelly. 
Rev. P. B. Brodie, J. Jones, Rev. E. 

Myers, H. C. Sorby, W. Pengelly. 
R. Etheridge, W. Pengelly, T. Wil- 
son, G. H. Wright. 
Edward Hull, W. Pengelly, Henry 

Woodward. 
Rev. 0. Fisher, Rev. J, Gunn, W. 

Pengelly, Eov. H. H. Wiuwood. 
W. Pengelly, W. Boyd Dawkins. 

Rev. n. H. Winwood. 
W. Pengelly, Rev. H. H. Winwood, 

W. Boyd Dawkins, G. H. Morton. 
R. Etheridge, J. Geikie, T. McKennv 

Hughes, L. C. Miall. 
L. C. Miall, George Scott, William 

Topley, Henry Woodward. 
L. C. Miall, R. H. Tiddeman, W. 

Topley. 

F. Drew, L. C. Jliall, R. G. Symes, 
R. H. Tiddeman. 

L. C. Miall, E. B. Tawney, W. Top- 
ley. 

J. Armstrong, F. W. Rudler, W. 
Topley. 

Dr. Le Neve Foster, R. H. Tidde- 
man, W. Topic)'. 

E. T. Hardman, Prof. J. O'Reill}-, 
R. H. Tiddeman. 

W. Topley, G. Blake Walker. 

W. Topley, W. Whitaker. 

J. E. Clark, W. Keeping, W. Topley, 
W. Whitaker. 

T. AV. Shore, W. Topley, E. West- 
lake, W. Whitaker. 

R. Betley, C. E. De Ranee, W. Top- 
ley, W. Whitaker. 

F. Adams, Prof. E. W. Claypole, W. 
Topley, W. Whitaker. 

C. E. De Ranee. J. Horne, J. J. H. 
1 Teall, W. Topley. 



BIOLOGICAL SCIENCES. 



COMMITTEE Of SCIENCES, IV. — ZOOLOGY, BOTANY, PHYSIOLOGY, ANATOMY. 

1832. Oxford lEev. P. B. Duncan, F.G.S. ...IRev. Prof. J. S. Henslow. 

1833. Cambridge' Rev. W. L. P. Garnons, F.L.S. ' C. C. Babinglon, D. Don. 

1834. Edinburgh. Prof. Graham |W. Yarrell, Prof. Burnett. 

' At this Meeting Physiology and Anatomy were made a separate Committee, 
for Presidents and Secretaries of which see p. li. 



PRESIDENTS AND SECBETAEIES OF THE SECTIONS. 
SECTION D. — ZOOLOGT AND BOTANY. 



xlix 



Date and Place 



Presidents 



1835. Dublin. 

1836. Bristol. 



Dr. Allman 

Rev. Prof. Henslow 



1837. Liverpool... 

1838. Newcastle 

1 839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 

1842. Manchester 



W. S. MacLeay 

Sir W. Jardine, Bart. 



Prof. Owen, F.R.S 

Sir W. J. Hooker, LL.D. 



1843. Cork. 

1844. York. 



1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 



John Richardson, M.D., F.R.S. 
Hon. and Very Rev. W. Her- 
bert, LL.D., F.L.S. 
William Tliompson, F.L.S. ... 

Very Rev. the Dean of Man- 
chester. 
'Rev. Prof. Henslow, F.L.S.... 
I Sir J. Richardson, M.D., 

j T? T? S 

H. E. Strickland, M.A., F.R.S. 



Secretaries 



J. Curtis, Dr. Litton. 

J. Curtis, Prof. Don, Dr. Riley, S. 

Eootsey. 
C. C. Babington, Rev. L. Jenyns, W. 

Swainson. 
J. E. Gray, Prof. Jones, R. Owen, 

Dr. Richardson. 
E. Forbes, W. Ick, R. Patterson. 
Prof. W. Couper, E. Forbes, R. Pat- 
terson. 
J. Couch, Dr. Lankester, R. Patterson. 
Dr. Lankester, E. Patterson, J. A. 

Turner. 
G. J. Allman, Dr. Lankester, R. 

Patterson. 
Prof. Allman, H. Goodsir, Dr. King, 

Dr. Lankester. 
Dr. Lankester, T. V. Wollaston, 
Dr. Lankester, T. V. Wollaston, H. 

Wooldridge. 
Dr. Lankester, Dr. Melville, T. V. 

Wollaston. 



1849. Birmingham 

1850. Edinburgh 

1851. Ipswich ... 

1852. Belfast 



1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 



1864. Bath 

1865. Birmingham 
1885. 



William Spence, F.R.S 

Prof. Goodsir, F.R.S. L. & E. 

Rev. Prof. Henslow, M.A., 

F.R.S. 
W. Ogilby 



SECTION D (contimied). — zooLoor and botany, including physiology. 

[For the Presidents and Secretaries of the Anatomical and Physiological Subsec- 
tions and the temporary Section E of Anatomy and Medicine, see p. li.] 

1848. Swansea ... L. W. Dillwyn, F.R.S Dr. R. Wilbraham Falconer, A. Hen- 

frey. Dr. Lankester. 
Dr. Lankester, Dr. Russell. 
Prof. J. H. Bennett, M.D., Dr. Lan- 
kester, Dr. Douglas Maclagan. 
Prof. Allman, F. W. Johnston, Dr. E. 

Lankester. 
Dr. Dickie, George C. Hyndman, Dr. 

Edwin Lankester. 
Robert Harrison, Dr. E. Lankester. 
Isaac Byerley, Dr. E. Lankester. 
William Keddie, Dr. Lankester. 
Dr. J. Abercrombie, Prof. Buckman, 

Dr. Lankester. 
Pro^:. J. R. Kinahan, Dr. E. Lankester, 

Robert Patterson, Dr. W. E. Steele. 
Henry Denny, Dr. Heaton, Dr. E. 

Lankester, Dr. E. Perceval Wright. 
Prof. Dickie, M.D., Dr. E. Lankester, 

Dr. Ogilvy. 
W. S. Church, Dr. E. Lankester, P, 

L. Sclater, Dr. E. Perceval Wright. 
Dr. T. Alcock, Dr. E. Lankester, Dr. 

P. L. Sclater, Dr. E. P. Wright. 
Alfred Newton, Dr. E. P. Wright. 
Dr. E. Charlton, A. Newton, Rev. H. 

B. Tristram, Dr. E. P. Wright. 
H. B. Brady, C. E. Broom," H. T. 

Stainton, Dr. E. P. Wright. 
Dr. J. Anthony, Rev. C. Clarke, Rev. 

H. B. Tristram, Dr. E. P. Wright. 
c 



C. C. Babington, M.A., F.R.S. 
Prof. Balfour, M.D., F.R.S.... 
Rev. Dr. Fleeming, F.R.S.E. 
Thomas Bell, F.R.S., Pres.L.S. 

Prof. W. H. Harvey, M.D., 

F.R.S. 
C. C. Babington, M.A., F.R.S. 

Sir W. Jardine, Bart., F.R.S.E. 

Rev. Prof. Henslow, F.L.S.... 

Prof. C. C. Babington, F.R.S. 

Prof . Huxley, F.R.S 

Prof. Balfour, M.D., F.R.S.... 

Dr. John E. Gray, F.R.S. ... 

T. Thomson, M.D., F.R.S. ... 



REPORT — 1885. 



SECTION D {continued). — biologt.' 



Date and Place 



1866. Nottingham 



1867. Dundee 



1868. Norwich 



1869. Exeter. 



1870. Liverpool. 



1871. Edinburgh 



1872. Brighton 



1873. Bradford 



1874, Belfast . 



1875. Bristol 



1876. Glasgow 



1877. Plymouth.. 



Presidents 



Prof. Hiixley, LL.D., F.R.S. 

— Pliijsiulo/i'ical Dcj>., Prof. 

Humphry," M.D., F.R.S.— 

Aiithropohf/ieal I)vp., Alf. 

K. Wallace, F.R.G.S. 
Prof. Sharpey, M.D., Sec. R.S. 

— Bcj). of Zool. and Bat., 

George Busk, M.D., F.K.8. 
Rev. M. J. Berkeley, F.L.S. 

— Dvp. of Physiohfiy, W. 

H. Flower, F.R.S. 

George P.usk, F.R.S., F.L.S. 
— -Dcp. of Hot. and Zool., 
C. Spence Bate, F.R.S. - 
Dc2>. of Ethno., E. B. Tylor. 

Prof.G. iRolle.ston,M.A., M.D., 
F.R.S., Y.l^.'S. — Bcj). of 
Aiiat. and P/ii/mil.,FTot.M. 
P'oster, M.D., F.L.S.— i>(y. 
of Ethno., J. Evans, F.R.S. 

Prof. Allen Thomson, M.D., 
¥.IX.^.—Dep. of Bot. and 
.^w*^.,rrof.WyvilleThomson, 
F.R.S.— Z'cy;. of Antfirojwl., 
Prof. W. Turner, M.D. 

Sir J. Lubbock, Bart., F.R.S.— 
Bej). of Anut. and Physiol., 
Dr. Burdon Sanderson, 
F.R.S.— Z)<y». ofAnthrojwl, 
Col. A. Lane Fox, F.G.S. 

Prof. Allman, F.R.S.— Brj>. of 
A nat.and Physiol. ,Vr:oi. Ru- 
therford, M.D. — Bvp-ofAn- 
thropol.. Dr. Beddoe, F.R.S. 

Prof. Redfern, M..V).—B(p. of 
Zool. and Bot., Dr. Hooker, 
C.B.,Pres.R.S.— i>(7Ao/^«- 
throp., Sir W.R.Wilde, M.D. 

P. L. Sclater, F.R.S.— Z**-^. o/ 
.1 nat.and Ph ifsiol.,Vr:oi.C\Q 
land, M.D., V.H.'&.—Bep.of 
Anthropol., Prof. Rolleston, 
M.D., F.R.S. 

A. Russel Wallace, F.R.G.S., 
F.L.S.— i?(y. of Zool. and 
Bot., Prof. A. Newton, M.A., 
¥.B,.S.—Bep. of Anat. and 
Phi/siol, Dr. J. G. McKen- 
drick, P.R.S.E. 

.J.awynJeffreys,LL.D.,F.R.S., 
F.L.S. — Bep. of Anat. and 
Phy.noL, Prof. Macalister, 



Secretaries 



Dr. J. Beddard, W. Felkin, Rev. H. 
B. Tristram, W. Turner, E. B. 
Tylor, Dr. E. P. Wright. 



C. Spence Bate, Dr. S. Cobbold, Dr. 
U. Foster, H. T. Stainton, Rev. H. 

B. Tristram, Prof. W. Turner. 
Dr. T. S. Cobbold, G. W. Firth, Dr. 

M. Foster, Prof. Lawson, H. T. 
Stainton, Rev. Dr. H. B. Tristram, 
Dr. E. P. Wrisrht. 

Dr. T. S. Cobbold, Prof. M. Foster, 
E. Ray Lankester, Prof. Lawson, 
H. T Stainton, Rev. H. B. Tris- 
tram. 

Dr. T. S. Cobbold, Sebastian Evans, 
Prof. Lawson, Thos. J. Moore, H. 
T. Stainton, Rev. H. B. Tri.stram, 

C. Staniland Wake, E. Ray Lan- 
kester. 

Dr. T. R. Eraser, Dr. Arthur Gamgee, 
E. Ray Lankester, Prof. Lawson, 
H. T. Stainton, C. Staniland Wake, 
Dr. W. Rutherford, Dr. Kelburne 
King. 

Prof. Thiselton-Dyer, H. T. Stainton, 
Prof. Lawson, F. W. Rudler, J. H. 
Lamprey, Dr. Gamgee, E. Ray 
Lankester, Dr. Pye-Smith. 

Prof. Thiselton-Dyer, Prof. Lawson, 
R. JI'Lachlan, Dr. Pye-Smith, E. 
Ray Lankester, F. W. Rudler, J. 
H. Lamprey. 

W.T. Thiselton- Dyer, R. O. Cunning- 
ham, Dr. J. J. Charles, Dr. P. H. 
Pye-Smith, J. J. Murphy, F. W. 
Rudler. 

E. R. Alston, Dr. McKendrick, Prof. 
W. R. M'Nab, Dr. Martyn, F. W. 
Rudler, Dr. P. H. Pye-Smith, Dr. 
W. Spencer. 

E. R. Alston, Hvde Clarke, Dr 
Knox, Prof. W." R. M'Nab, Dr. 
Muirhead, Prof. Morrison Wat- 
son. 



E. R. Alston, F. Brent, Dr. D. J 
Cunningham, Dr. C. A. Hingston, 
Prof. W. R. M'Nab, J. B. Rowe, 
F. W. Rudler. 



M.D.~Bep. of Anthropol., 
Francis Galton, M.A.,F.R.S. 

' At a meeting of the General Committee in 1865, it was resolved : — ' That the title 
of Section D be changed to Biology ; ' and ' That for the word " Subsection," in the 
rules for conducting thebusiness of the Sections, the word "Department" be substituted.' 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



li 



Date and Place 



1878. Dublin , 



1879. Sheffield ... 



1880. Swansea 



1881. York. 



1882. Southamp- 
ton. 



1883. Southport' 

1884. Montreal-... 

1885. Aberdeen... 



'Presidents 



Prof. W. H. Flower, F.R.S.— 

Bcp. of AnthrojMl., Prof. 

Huxley, Sec. R.S. — Bip. 

of A/iat. and Physiol., R. 

McDonnell, M.D., F.R.S. 
Prof. St. George Mivart, 

F.R.S.— Z)e/A 4 Anthropol., 

E. B. Tylor, D.C.L., F.R.S. 
— Bep. of Anat. and Phi/- 
mil.. Dr. Pye-Smith. 

A. C. L. Giinther, M.D., F.R.S. 
— Dcp. of Anat. and Phy- 
siol, F. M. Balfour, M.A., 
F.'R.S.—Bep. of Antkropol., 

F. W. Rudler, F.G.S. 
Richard Owen, C.B., M.D., 

F.R.S.^Bep.of AnthropoL, 
Prof. W. H. Flower, LL.D., 
F.R.S.— 2)<7A of Anat. and 
Phymol.,YToi.J. S. Burden 
Sanderson, M.D., F.R.S. 

Prof. A. Gamgee, M.D., F.R.S. 
- Bep. of Zool. and Bot., 
Prof. M. A. Lawson, M.A., 
F.Jj.S.— Bep. of Anthropol., 
Prof. W. Boyd Dawkins, 
M.A., F.R.S. 

Prof. E. Ray Lankester, M.A., 
F.R.S.— D^jy;. of Anthropol., 
W. Pengelly, F.R.S. 

Prof. H. N. Moseley, M.A., 

F.R.S. 
Prof. W. C. Mcintosh, M.D., 

LL.D., F.R.S. L. & E. 



Secretaries 



Dr. R. J. Harvey, Dr. T. Hayden, 
Prof. W. R. M'Nab, Prof. J. M. 
Purser, J. B . Rowe, F. W. Rudler. 



Arthur Jackson, Prof. W. R. M'Nab, 
J. B. Rowe, F. W. Rudler, Prof. 
Schiifer. 



G. W. Bloxam, John Priestley, 
Howard Saunders, Adam Sedg- 
wick. 



G. W. Bloxam, W. A. Forbes, Rev. 
W. C. Hey, Prof. W. R. M'Nab, 
W. North, John Priestley, Howard 
Saunders, H. E. Spencer. 



G. W. Bloxam, W. Heape, J. B. 
Nias, Howard Saunders, A. Sedg- 
wick, T. W. Shore, jun. 



G. W. Bloxam, Dr. G. J. Haslam, 
W. Heape, W. Hurst, Prof. A. M. 
Marshall, Howard Saunders, Dr. 
G. A. Woods. 

Prof. W. Osier, Howard Saunders, A. 
Sedgwick, Prof. R. R. Wright. 

W. Heape, J. McGregor- Robertson, 
J. Duncan Matthews, Howard 
Saunders, H. Marshall Ward. 



ANATOMICAL AND PHYSIOLOGICAL SCIENCES. 

COMMITTEE OF SCIENCES, V. — ANATOMY AND PHYSIOLOGY. 

1833. Cambridge |Dr. Haviland iDr. Bond, Mr. Paget. 

1834. Edinburgh |Dr. Abercrombie iDr. Roget, Dr. William Thomson. 

SECTION E (until 1847). — ANATOMY AND MEDICINE. 



183.5. Dublin 

1836. Bristol 

1887. Liverpool... 

1838. Newcastle 

1839. Birmingham 

1840. Glasgow ... 

1841. Plymouth... 



Dr. Pritchard 

Dr. Roget, F.R.S 

Prof. W. Clark, M.D. 



T. E. Headlam, M.D 

John Yelloly, M.D., F.R.S... 
James Watson, M.D 

P. M. Roget, M.D., Sec. R.S. 



Dr. Harrison, Dr. Hart. 

Dr. Symonds. 

Dr. J. Carson, jun., James Long, 

Dr. J. R. W. Vose. 
T. M. Greenhow, Dr. J. R. W. Vose. 
Dr. G. O. Rees, F. Ryland. 
Dr. J. Brown, Prof. Couper, Prof 

Reid. 
Dr. J. Butter, J. Fuge, Dr. R. R 

Sargent. 



' By direction of the General Committee at Southampton (1882) the Departments 
■of Zoology and Botany and of Anatomy and Physiology were amalgamated. 

-By authority of the General Committee, Anthropology was made a separate 
Section, for Presidents and Secretaries of which see p. Ivii. 

c2 



lii 



REPORT 1885. 



SECTION E. PHYSIOLOGY. 



Date and Place 



1842. Manchester 

1843. Cork 

1844 York 

1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford' ... 



Presidents 



Secretaries 



Edward Holme, M.D., F.L.S.'Dr. Cliaytor, Dr. R. S. Sargent. 



Sir James Pitcairn, M.D. 

J. C. Pritchard, M.D 

Prof. J. Haviland, M.D. . 
Prof. Owen, M.D., F.R.S. 

Prof. Ogle, M.D., F.R.S. . 



Dr. John Popham, Dr. R. S. Sargent. 

I. Erichsen, Dr. R. S. Sargent. 

Dr. R. S. Sargent, Dr. Webster. 

C. P. Keele, Dr. Laycock, Dr. Sar- 
gent. 

Dr. Thomas K. Chambers, W. P. 
Ormerod. 



1850. 
1855. 
1857. 

1858, 

1859. 
1860. 

1861. 
1862. 
1863. 
1864. 

1865. 



Edinburgh 
Glasgow ... 

Dublin 

Leeds 

Aberdeen... 
Oxford 

Manchester 
Cambridge 
Newcastle 
Bath 

Birming- 
ham.^ 



PHYSIOLOGICAL SUBSECTIONS OF SECTION D. 

Prof. Bennett, M.D., F.R.S.E. 
Prof. Allen Tliomson, F.R.S. 

Prof. R. Harrison, M.D 

Sir Benjamin Brodie, Bart., 

F.R.S. 
Prof. Sliarpev, M.D., Sec.R.S. 
Prof. G. RoUeston, M.D., 

F.L.S. 
Dr. John Davy, F.R.S.L.& E. 

G. E. Paget, M.D 

Prof. Rolleston, M.D., F.R.S. 
Dr. Edward Smith, LL.D., 

F.R.S. 
Prof. Acland, M.D., LL.D., 

F.R.S. 



Prof. J. H. Corbett, Dr. J. Struthers. 
Dr. R. D. Lyons, Prof. Redfern. 
C. G. Wheelhouse. 

Prof. Bennett, Prof. Redfern. 

Dr. R. M'Donnell, Dr. Edward 

Smith. 
Dr. W. Roberts, Dr. Edward Smith. 
G. F. Helm, Dr. Edward Smith. 
Dr. D. Embleton, Dr. W. Turner. 
J. S. Bartrum, Dr. W. Turner. 

Dr. A. Fleming, Dr. P. Hesiop, 
Oliver Pembleton, Dr. W. Turner. 



GEOGRAPHICAL AND ETHNOLOGICAL SCIENCES. 

[For Presidents and Secretaries for Geography previous to 1851, see Section C, , 
p. xlvi.] 

ETHNOLOGICAL SUBSECTIONS OF SECTION D. 



1846. Southampton 

1847. Oxford 

1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 



Dr. Pritcliard Dr. King. 



Prof. H. H. Wilson, M.A. 



Prof. Buckley. 
G. Grant Francis. 
Dr. R. G. Latham. 
Daniel Wilson. 



Vice-Admiral Sir A. Malcolm 
SECTION E. — GEOGRAPHY AND ETHNOLOGY. 



R. Cull, Rev. J. W. Donaldson, Dr. 

Norton Shaw. 
R. Cull, R. MacAdam, Dr. Norton 

Shaw. 
R. Cull, Rev. H. W. Kemp, Dr. 

Norton Shaw. 
Richard Cull, Rev. H. Higgins, Dr. 

Hine, Dr. Norton Shaw. 
Dr. W. G. Blackie, R. Cull, Dr. 

Norton Shaw. 
R. Cull, F. D. Hartland, W. H. 

Rumsey, Dr. Norton Shaw. 
R. Cull, S. Ferguson, Dr. R. R. 

Madden, Dr. Norton Shaw. 

' By direction of the General Committee at Oxford, Sections D and E were 
incorporated under tlic name of ' Section D — Zoology and Botany, including Phy- 
siology ' (see p. xlix). The Section lieing then vacant was assigned in 1851 to 
Geography. * Vide note on page 1. 



1851. 


Ipswich ... 


1852. 


Belfast 


1853. 


Hull 


1854. 


Livei-pool... 


18.55. 


Glasgow ... 


1856. 


Cheltenham 


1857. 


Dublin 



Sir R. I. Murchison, F.R.S., 

Pres. R.G.S. 
Col. Chesney, R.A., D.C.L., 

F.R.S. 
R. G. Latham, M.D., F.R.S. 

Sir R. I. Murchison, D.C.L., 

F.R.S. 
Sir J. Richardson, M.D., 

F.R.S. 
Col. Sir H. C. Rawlinson, 

K.C.B. 
Rev. Dr. J. Henthorn Todd, 

Pres. R.I.A. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



liii 



Date and Place 



1858. Leeds 



1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee ... 

1868. Norwich ... 



Presidents 



Sir R.I. Mm-chison,G.C.St.S., 
F.R.S. 

Rear - Admiral Sir James 
Clerk Ross, D.C.L., F.R.S. 

Sir R. I. Murchison, D.C.L.. 
F.R.S. 

John Crawfvird, F.R.S 

Francis Galton, F.R.S 



Sir R. I. Murchison, K.C.B., 

F.R.S. 
Sir R. I. Murchison, K.C.B., 

F.R.S. 
Major-General Sir H. Raw- 

linson, M.P., K.C.B., F.R.S. 
Sir Charles Nicholson, Bart.. 

LL.D. 

Sir Samuel Baker, F.R.G.S. 



Capt. G. H. Richards, R.X. 
F.R.S. 



Secretaries 



R. Cull, Francis Galton, P. O'Cal- 
laghan. Dr. Norton Shaw, Thomas 
Wright. 

Richard Cull, Prof.Geddes, Dr. Nor- 
ton Shaw. 

Capt. Burrows, Dr. J. Himt, Dr. C. 
Lempri^re, Dr. Norton Shaw. 

Dr. J. Hunt, J. Kingsley, Dr. Nor- 
ton Shaw, W. Spottiswoode. 

J. W. Clarke, Rev. J. Glover, Dr. 
Hunt, Dr. Norton Shaw, T. 
Wright. 

C. Carter Blake, Hume Greenfield, 

C. R. Markham, R. S. Watson. 

H. W. Bates, C. R. Markham, Capt, 
R. M. Murchison, T. Wright. 

H. W. Bates, S. Evans, G. Jabet, C. 
R. Markham, Thomas Wright. 

H. W. Bates, Rev. E. T. Cusins, R. 
H. Major, Clements R. JIarkham, 

D. W. Nash, T. Wright. 

H. W. Bates, Cyril Graham, Clements 
R. Markham, S. J. Mackie, R. 
Sturrock. 

T. Baines, H. W. Bates, Clements R. 
Markham, T. Wright. 



1869. Exeter 

1870. Liverpool.. 

1871. Edinburgh 

1872. Brighton.. 

1873. Bradford.. 

1874. Belfast 

1875. Bristol 

1876. Glasgow .. 

1877. Plymouth.. 

1878. Dublin 

1879. Sheffield .. 

1880. Swansea .. 

1881. York 

1882. Southamp- 

ton. 



SECTION E {continued). - 

Sir Bartle Frere, K.C.B., 

LL.D., F.R.G.S. 
Sir R. I.Murcbison,Bt.,K.C.B., 
LL.D., D.C.L., F.R.S., F.G.S. 
Colonel Yule, C.B., F.R.G.S. 

Francis Galton, F.R.S 

Sir Rutherford Alcock, K. C.B. 

Major Wilson, R.E., F.R.S., 

F.R.G.S. 
Lieut. - General Strachey, 

R.E.,C.S.I.,F.R.S.,F.R.G.S., 

F.L.S., F.G.S. 
Capt. Evans, C.B., F.R.S 

Adm.SirE. Ommanney, C.B., 
F.R.S., F.R.G.S., F.R.A.S. 

Prof. Sir C. Wyville Thom- 
son, LL.D., F.R.S.L.&E. 

Clements R. Markham, C.B., 
F.R.S., Sec. R.G.S. 

Lieut.-Gen. Sir J. H. Lefroy, 
C.B., K.C.M.G., R.A., F.R.S., 

Th' T? P S 

Sir J. b.' Hooker, K.C.S.L, 

C.B., F.R.S. 
Sir R. Temple, Bart., G.C.S.I., 

F.R.G.S. 



-GEOGRAPHY. 

H. W. Bates, Clements R. Markham, 

J. H. Thomas. 
H.W.Bates, David Buxton, Albert J. 

Mott, Clements R. Markham. 
Clements R. Markham, A. Buchan, 

J. H. Thomas, A. Keith Johnston. 
H. W. Bates, A. Keith Johnston, 

Rev. J. Newton, J. H. Thomas. 
H. W. Bates, A. Keith Johnston, 

Clements R. Markham. 
E. G. Ravenstein, E. C. Rye, J. H. 

Thomas. 
H. W. Bates, E. C. Rye, F. F. 

Tuckett. 

H. W. Bates, E. C. Rye, R. Oliphant 

Wood. 
H. W. Bates, F. E. Fox, E. C. Rye. 

John Coles, E. C. Rye. 

H. W. Bates, C. B. D. Black, E. C. 

Rye. 
H. W. Bates, E. C. Rye. 



J. W. Barry, H. W. Bates. 
E. G. Ravenstein, E. C. Eye. 



liv 



EEPORT — 1885. 



Date and Place 



Presidents 



Secretaries 



1883. Southport 

1884. Montreal .. 

1885. Aberdeen., 



Lieut.-Col. H. H. Godwin- 
I Austen, F.R.S. 
Gen. Sir J. H. Lefroy, C'.B., 

K.C.M.G., F.R.S.,Y.P.R.G.S. 
Gen. J. T. Walker, C.B., R.E., 

LL.D., F.E.S. 



John Coles, E. G. Eavenstein, E. C. 

Rye. 
Rev. Abbe Laflamme, J. S. O'Halloran, 

E. G. Ravenstein, J. F. Torrance 
J. S. Keltie, J. S. O'Halloran, E. G. 

Ravenstein, Rev. G. A. Smith. 



1833. 
1834, 



STATISTICAL SCIENCE. 

COMMITTEE OF SCIENCES, VI. — STATISTICS. 

Cambridge! Prof. Babbage, F.R.S i J. E. Drinkwater. 

Edinburgh I Sir Charles Lemon, Bart | Dr. Cleland, C. Hope Maclean. 



SECTION F.— STATISTICS. 



1835. 
1836. 

1837. 

1838. 
1839. 

1840. 

1841 

1842. 

1843. 
1844. 

1845. 
1846. 

1847. 

1848. 
1849. 

1850. 

1851. 
1852. 

1853. 
1854. 

1855. 



Dublin 

Bristol 

Liverpool... 

Newcastle 
Birmingham 

Glasgow ... 

Pljinouth... 

Manchester 

Cork 

York 

Cambridge 
Southamp- 
ton. 
Oxford 

Swansea ... 
Birmingham 

Edinburgh 

Ipswich ... 
Belfast 

Hull 

Liverpool... 

Glasgow ... 



Charles Babbage, F.R.S 

Sir Chas. Lemon, Bart., F.R.S. 

Rt. Hon. Lord Sandon 

Colonel Sykes, F.R.S 

Henry Hallam, F.R.S 

Rt. Hon. Lord Sandon, M.P., 

F.R.S. 
Lieut.-Col. Sykes, F.R.S 

G. W. Wood, M.P., F.L.S. ... 

Sir C. Lemon, Bart., M.P. ... 
Lieut. - Col. Sykes, F.R.S., 

F.L.S. 
Rt.Hon. the Earl Fitzwilliam 
G. R. Porter, F.R.S 



Travers Twiss, D.C.L.. F.R.S, 

J. H, Vivian, M.P., F.R.S. ... 
Rt. Hon. Lord Lyttelton 



Very Rev. Dr. John Lee, 

V.P.R.S.E. 
Sir John P. Boileau, Bart. ... 
His Grace the Archbishop of 

Dublin. 
James Heywood, M.P., F.R.S. 
Thomas Tooke, F.R.S 

R. Monckton Milnes, M.P. ... 



W. Greg, Prof. Longfield. 

Rev. J. E. Bromby, C. B. Fripp,. 

James Heywood. 
W. R. Greg, W. Langton, Dr. W. C. 

Tayler. 
W. Cargill, J. Heywood, W.R.Wood. 
F. Clarke, R. W. Rawson, Dr. W. C. 

Tayler. 
C. R. Baird, Prof. Ramsay, E. W. 

Rawson. 
Rev. Dr. Byrth, Rev. R. Luney, R. 

W. Rawson. 
Rev. R. Luney, G. W. Ormerod, Dr. 

W. C. Tayler. 
Dr. D. Bullen, Dr. W. Cooke Tayler.. 
J. Fletcher, J. Heywood, Dr. Lay- 
cock. 
J. Fletcher, Dr. W. Cooke Tayler. 
J. Fletcher, F. G. P. Neison, Dr. W. 

C. Tayler, Rev. T. L. Shapcott. 
Rev. W. H. Cox, J. J. Danson, F. G. 

P. Neison. 
J. Fletcher, Capt. R. Shortrede. 
Dr. Finch, Prof. Hancock, F. G. P. 

Neison. 
Prof. Hancock, J. Fletcher, Dr. J. 

Stark. 
J. Fletcher, Prof. Hancock. 
Prof. Hancock, Prof. Ingram, James 

MacAdam, jun. 
Edward Cheshire, W. Newmarch. 
B. Cheshire, J. T. Danson, Dr. W. H. 

Duncan, W. Newmarch. 
J. A. Campbell, E. Cheshire, W. New- 
march, Prof. R. H. Walsh. 



SECTION F (continued). — economic science ani> statistics. 



1856. Cheltenham 

1857. Dublin 



Rt. Hon. Lord Stanley, M.P. 



His Grace the Archbishop of 
Dublin, M.R.LA. 



Rev. C. H. Bromby, E. Cheshire, Dr 
W. N. Hancock, W. Newmarch, W- 
M. Tartt. 

Prof. Cairns, Dr. H. D. Hutton, W.. 
Newmarch. 



PRESIDENTS AND SECEETAEIES OF THE SECTIONS. 



iv 



Date and Place 



Presidents 



Secretaries 



1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle . 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee 

1868. Norwich.... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton... 
187.3. Bradford ... 

1874. Belfast 

1875. Bristol 

1876. Glasgow ... 

1877. Plymouth... 

1878. Dublin 

1879. Sheffield ... 

1880. Swansea ... 

1881. York 

1882. Southamp- 

ton. 

1883. Southport 

1884. Montreal ... 

1885. Aberdeen... 



Edward Baines 

Col. Sykes, M.P., F.R.S 

Nassau W. Senior, M.A 

William Ne^vmarch, F.R.S... . 



Edwin Chadwick, C.B 

William Tite, M.P., F.R.S. ... 

William Farr, M.D., D.C.L., 

F.R.S. 
Rt. Hon. Lord Stanley, LL.D., 

M.P. 
Prof. J. E. T. Rogers 



M. E. Grant Duff, M.P 

Samuel Brown, Pres. Instit. 
Actuaries. 

Rt . Hon. Sir Stafford H. North- 
cote, Bart., C.B., M.P. 

Prof. W. Stanley Jevons, M.A. 

Rt. Hon. Lord Neaves 

Prof. Henry Fawcett, M.P. ... 
Rt. Hon. W. E. Forster, M.P. 
Lord O'Hagan 



James Heywood, M.A., F.R.S., 

Pres.S.S. 
Sir George Campbell, K.C.S.L, 

M.P. 
Rt. Hon. the Earl Fortescue 
Prof. J. K. Ingram, LL.D., 

M.R.LA. 
G. Shaw Lefevre, M.P., Pres. 

S.S. 

G. W. Hastings, M.P 

Rt. Hon. M. E. Grant-Duff, 

M.A., F.R.S. 
Rt. Hon. G. Sclater-Booth, 

M.P., F.R.S. 
R. H. Inglis Palgrave, F.R.S. 

Sir Richard Temple, Bart., 
G.C.S.L, CLE., F.R.G.S. 

Prof. H. Sidgwick, LL.D., 
Litt.D. 



T. B. Baines, Prof. Cairns, S. Brown, 

Capt. Fishbourne, Dr. J. Strang. 
Prof. Cairns, Edmund Macrory, A. M. 

Smith, Dr. John Strang. 
Edmund Macrory, W. Newmarch, 

Rev. Prof. J. E. T. Rogers. 
David Chadwick, Prof. R. C. Christie, 

E. Macrory, Rev. Prof. J. E. T. 

Rogers. 
H. D. Macleod, Edmund Macrory. 
T. Doubleday, Edmund Macrory 

Frederick Purdy, James Potts. 

E. Macrory, E, T. Payne. F. Purdy. 

G. J. D. Goodman, G. J. Johnston, 

E. Macrory. 
R. Birkin, jun., Prof. Leone Levi, E. 

Macrory. 
Prof. Leone Levi, E. Macrory, A. J. 

Warden. 
Rev. W. C. Davie, Prof, Leone Levi. 

Edmund Macrory, Frederick Purdy, 

Charles T. D. Acland. 
Chas. R. Dudley Baxter, E. Macrory, 

J. Miles Moss. 
J. G. Fitch, James Meikle. 
J. G. Fitch, Barclay Phillips. 
J. G. Fitch, Swire Smith. 
Prof. Donnell, Frank P. Fellows, 

Hans MacMordie. 

F. P. Fellows, T. G. P. Hallett, B. 
Macrory. 

A. M'Neel Caird, T. G. P. Hallett, Dr. 

W. Neilson Hancock, Dr. W. Jack. 

W. F. Collier, P. Hallett, J. T. Pirn, 

W. J. Hancock, C. Molloy, J. T. Pirn. 

Prof. Adamson, R. E. Leader, C. 

Molloy. 
N. A. Humphreys, C. Molloy. 
C. Molloy, W. W. Morrell, J. F. 

Moss. 

G. Baden- Powell, Prof. H. S. Fox- 
well, A. Milnes, C. Molloy. 

Rev. W. Cunningham, Prof. H. S. 

Foxwell, J. N. Keynes, C. Molloy. 
Prof. H. S. Foxwell, J. S. McLennan, 

Prof. J. Watson. 
Rev. W. Cunningham, Prof. H. S. 

Foxwell, C. McCombie, J. P. Moss. 



1836. Bristol 

1837. Liverpool.. 

1838. Newcastle 



MECHANICAL SCIENCE. 

SECTION G. — MECHANICAL SCIENCE. 



Davies Gilbert, D.C.L., F.R.S. 

Rev. Dr. Robinson 

Charles Babbage, F.R.S 



T. G. Bunt, G. T. Clark, W. West. 
Charles Vignoles, Thomas Webster. 
R. Hawthorn, C. Vignoles, T. 
Webster. 



Ivi 



REPORT 1885. 



Date and Place 

1839. Binningham 

1840. Glasgow .... 

1841. Plymouth 

1842. Manchester 

1843. Cork 

1844. York 

1845. Cambridge 

1846. Southamp- 

ton. 

1847. Oxford 

1848. Swansea ... 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich 

1852. Belfast 

1853. Hull 

1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 

1857. Dublin 

1858. Leeds 

1859. Aberdeen... 

1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 

1864. Bath 

1865. Birmingham 

1866. Nottingham 

1867. Dundee 

1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton ... 

1873. Bradford ... 

1874. Belfast 



Presidents 



Prof. Willis, F.K.S., and Robt. 

Stephenson. 
Sir John Robinson 



John Taylor, F.R.S 

Rev. Prof. Willis, F.R.S 

Prof. J. Macneill, M.R.LA.... 

John Taylor, F.R.S 

George Rennie, F.R.S 

Rev. Prof. Willis, M.A., F.R.S. 

Rev. Prof .Walker, M.A.,F.R.S. 
Rev. Prof .Walker, M.A.,F.R.S. 
Robert Stephenson, M.P., 

F.R.S. 

Rev. R. Robinson 

William Cubitt, F.R.S 

John Walker, C.E., LL.D., 

F.R.S. 
William Fairbairn, C.E., 

F.R.S. 
John Scott Russell, F.R.S. ... 

W. J. JTacquorn Rankine, 

C.E., F.R.S. 
George Rennie, F.R.S 



Rt. Hon. the Earl of Rosse, 

F.R.S. 
William Fairbairn, F.R.S. ... 
Rev. Prof. Willis, M.A., F.R.S. 

Prof . W. J. Macquorn Rankine, 

LL.D., F.R.S. 
J. F. Bateman, C.E., F.R.S.... 

Wm. Fairbairn, LL.D., F.R.S. 
Rev. Prof. Willis, M. A., F.R.S. 

J. Hawkshaw, F.R.S 

Sir W. G. Armstrong, LL.D., 

F.R.S. 
Thomas Hawksley, V.P.Inst. 

C.E., F.G.S. 
Prof.W. J. Macquorn Rankine, 

LL.D., F.R.S. 
G. P. Bidder, C.E., F.R.G.S. 

C. W. Siemens, F.R.S 

Chas. B. Vignoles, C.E., F.R.S. 

Prof. Fleeming Jenkin, F.R.S. 

F. J. Bramwell, C.E 

W. H. Barlow, F.R.S 



Prof. James Thomson, LL.D. 
C.E., F.R.S.E. 



Secretaries 



W. Carpmael, William Hawkes, T. 

Webster. 
J. Scott Russell, J. Thomson, J. Tod, 

C. Vignoles. 
Henry Chat field, Thomas Webster. 
J. F. Bateman, .J. Scott Russell, J, 

Thomson, Charles Vignoles. 
James Thomson, Robert Mallet. 
Charles Vignoles, Thomas Webster. 
Rev. W. T. Kingsley. 
William Betts, jun., Charles Manby. 

J. Glynn, R. A. Le Mesurier. 
R. A. Le Mesurier, W. P. Struvd. 
Charles Manby, W. P. Marshall. 

Dr. Lees, David Stephenson. 

John Head, Charles Manby. 

John F. Bateman, C. B Hancock, 

Cliarles Manby, James Thomson. 
James Oldliam, J. Thomson, W. 

Sykes Ward. 
John Grantham, J. Oldham, J, 

Thomson. 
L. Hill, jun., William Ramsay, J. 

Thomson. 
C. Atherton, B. Jones, jun., H. M. 

Jeffery. 
Prof. Downing, W.T. Doyne, A. Tate, 

James Thomson, Henry Wright. 
J. C. Dennis, J. Dixon, H. Wright. 
R. Abernethj", P. Le Neve Foster, H. 

Wright. 
P. Le Neve Foster, Rev. F. Harrison, 

Henry Wright. 
P. Le Neve Foster, John Robinson, 

H. Wright. 
W. JL Fawcett, P. Le Neve Foster. 
P. Le Neve Foster, P. Westmacott, 

J. F. Spencer. 
P. Le Neve Foster, Robert Pitt. 
P. Le Neve Foster, Henry Lea, W. 

P. Marshall, Walter May. 
P. Le Neve Foster, J. F. Iselin, M. 

0. Tarbotton. 
P. Le Neve Foster, John P. Smith, 

W. W. Urquliart. 
P. Le Neve Foster, J. F. Iselin, C. 

Manby, W. Smith. 
P. Le Neve Foster, H. Bauerman. 
H. Bauerman, P. Le Neve Foster, T. 

King, J. N. Shoolbred. 
H. Bauerman, Alexander Leslie, J. 

P. Smith. 
H. M. Brunei, P. Le Neve Foster, 

J. G. Gamble, J. N. Shoolbred. 
Crawford Barlow, H. Bauerman, 

E. H. Carbutt, J. C. Hawkshaw, 

J. N. Shoolbred. 
A. T. Atchison, J. N. Shoolbred, John 

Smyth, jun. 



PRESIDENTS AND SECRETARIES OF THE SECTIONS. 



Ivii 



Date and Place 

1875. Bristol 

1876. Glasgow .. 

1877. Plj-mouth.. 

1878. Dublin 

1879. Sheffield .. 

1880. Swansea .. 

1881. York 



Presidents 



Secretaries 



1882. Southamp- 

ton. 

1883. Southport 

1884. Montreal .. 

1885. Aberdeen.. 



W. Froude, C.E., M.A., F.R.S. 

C. W. Merrifield, F.R.S 

Edward Woods, C.E 

Edward Easton, C.E 

J. Robinson, Pres. Inst. Mech. 

Eng. 
James Abernethy, V.P.Inst. 

O.E., F.R.S.E. 
Sir W. G. Armstrong, C.B., 

LL.D., D.C.L., F.R.S. 
John Fowler, C.E., F.G.S. ... 

James Brunlees, F.R.S.E., 

Pres.Inst.C.E. 
Sir F. J. Bramwell, F.R.S., 

V.I'.Inst.C.E. 
B. Baker, M.Inst.C.E 



W. R. Browne, H. M. Brimel, J. G. 

Gamble, J. N. Shoolbred. 
W. Bottomlev, jun., W. J. Millar, 

J. N. Shoolbred, J. P. Smith. 
A. T. Atchison, Dr. Merrifield, J. N. 

Shoolbred. 
A. T. Atchison, R. G. Symes, H. T. 

Wood. 
A. T. Atchison, Emerson Bainbridge, 

H. T. Wood. 
A. T. Atchison, H. T. Wood. 

A. T. Atchison, J. F. Stephenson, 

H. T. Wood. 
A. i'. Atchison, F. Ghurton, H. T. 

Wood. 
A. T. Atchison, E. Rigg, H. T. Wood. 

A. T. Atchison, W. B. Dawson, J. 

Kennedy, H. T. Wood. 
A. T. Atchison, F. G. Ogilvie, E. 

Rigg, J. N. Shoolbred. 



ANTHROPOLOGICAL SCIENCE. 



1884. Montreal.. 

1885. Aberdeen.. 



SECTION H. — ANTHROPOLOGY. 



E. B. Tylor, D.C.L., F.R.S. ... 
Francis Galton, MA., F.R.S. 



G. W. Bloxam, W. Hurst. 
G. W. Bloxam, Dr. J. G. Garson, W. 
Hurst, Dr. A. Macgregor. 



LIST OF EVENING LECTURES. 



Date and Place 



1842. Manchester 



J1843. Cork 



1844. York , 



1845. Cambridge 

1846. Southamp- 

ton, 



1847. Oxford. 



Lecturer 



Charles Vignoles, F.R.S. . 



Sir M. I. Brunei 

R. I. Murchison 

Prof. Owen, M.D., F.R.S... 
Prof. E. Forbes, F.R.S 



Dr. Robinson 

Charles Lyell, F.R.S 

Dr. Falconer, F.R.S 

G.B.Airy,F.R.S.,Astron.Royal 

R. I. Murchison, F.R.S 

Prof. Owen, M.D., F.R.S. ... 

Charles Lyell, F.R.S 

W. R. Grove, F.R.S 



Rev. Prof. B. Powell, F.R.S. 
Prof. M. Faraday, F.R.S 

Hugh E. Strickland, F.G.S... . 



Subject of Discourse 



The Principles and Construction of 
Atmospheric Railways, 

The Thames Tunnel. 

The Geology of Russia. 

The Dinornis of New Zealand. 

The Distribution of Animal Life in 
the ^gean Sea. 

The Earl of Rosse's Telescope. 

Geology of North America. 

The Gigantic Tortoise of the Siwalik 
Hills in India. 

Progress of Terrestrial Magnetism. 

Geology of Russia. 

Fossil Mammalia of the British Isles. 

Valley and Delta of the Mississippi. 

Properties of the Explosive substance 
discovered by Dr. Schonbein ; also 
some Researches of his own on the 
Decomposition of Water by Heat. 

Shooting Stars. 

Magnetic and Diamagnetic Pheno- 
mena. 

The Dodo {Bidus ineptus). 



Iviii 



REPORT 1885. 



Date and Place 



1848. Swansea , 

1849. Birmingham 

1850. Edinburgh 

1851. Ipswich .. 

1852. Belfast 



1853, Hull. 



1854. Liverpool... 

1855. Glasgow ... 

1856. Cheltenham 



Lecturer 



1857. Dublin.... 

1858. Leeds .... 

1859. Aberdeen. 



1860. Oxford 

1861. Manchester 

1862. Cambridge 

1863. Newcastle 



1864. Bath 

1865. Birmingham 

1866. Nottingham 



John Percy, M.D., F.R.S 

W. Carpenter, M.D., F.R.S... . 

Dr. Faraday, F.K.S 

Rev. Prof. Willis, M.A., F.R.S. 

Prof. J. H. Bennett, M.D., 
F.R.S.E. 

Dr. Mantell, F.R.S 

Prof. R. Owen, M.D., F.R.S. 

G.B.Airy,F.R.S.,Astron. Royal 
Prof. G. G. Stokes, D.C.L., 

F.R.S. 
Colonel Portlock, R.E., F.R.S. 



Prof. J. Phillips, LL.D., F.R.S., 
F.G.S. 

Robert Hunt, F.R.S 

Prof. R. Owen, M.D., F.R.S. 
Col. E. Sabine, V.P.R.S 

Dr. W. B. Carpenter, F.R.S. 
Lieut.-Col. H. Rawlinson ... 



Col. Sir H. Rawlinson 



W. R. Grove, F.R.S 

Prof. W. Thomson, F.R.S. ... 
Rev. Dr. Livingstone, D.C.L. 
Prof. J. Phillips,LL.D.,F.R.S. 
Prof. R. Owen, M.D., F.R.S. 
Sir R. I. Murchison, D.C.L... . 
Rev. Dr. Robinson, F.R.S. ... 

Rev. Prof. Walker, F.R.S. ... 
Captain Sherard Osborn, R.N. 
Prof. W. A. Miller, M.A., F.R.S. 
G.B.Airy,F.R.S.,Astron.Royal 
Prof. Tyndall, LL.D., F.R.S. 

Prof. Odliug, F.R.S 

Prof. Williamson, F.R.S 



James Glaisher, F.R.S., 

Prof. Roscoe, F.R.S 

Dr. Livingstone, F.R.S. 
J. Beete Jukes, F.R.S. .. 



William Huggins, F.R.S. ... 
Dr. J. D. Hooker, F.R.S 



Subject of Discourse 



Metallurgical Operations of Swansea 
and its neighbourhood. 

Recent Microscopical Discoveries. 
Mr. Gassiot's Battery. 

Transit of diiferent Weights with 
varying velocities on Railways. 

Passage of tlie Blood through the 
minute vessels of Animals in con- 
nexion with Nutrition. 

Extinct Birds of New Zealand. 

Disi inct ion between Plants and Ani- 
mals, and tlieir changes of Form. 

Total Solar Eclipse of July 28, 1851. 

Recent discoveries intlie properties 
of Light. 

Recent discovery of Rock-salt at 
Carrickfergus, and geological and 
pract ical considerations connected 
with it. 

Some peculiar Phenomena in the 
Geohigy and Physical Geography 
of Yorkshire. 

The present state of Photography. 

Anthropomorphous Apes. 

Progress of researches in Terrestrial 
Magnetism. 

Characters of Species. 

Ass3Tian and P>abylonian Antiquities 
and Etlinology. 

Recent Discoveries in Assyi'ia and 
Babylonia, v^^ith the results of 
Cuneiform research up to the 
present time. 

Correlation of Plij'sical Forces. 

The Atlantic Telegraph. 

Recent Discoveries in Africa. 

The Ironstones of Yorkshire. 

The Fossil Mammalia of Australia. 

Geology of the Nortliern Highlands. 

Electrical Discharges in highly 
rarefied Media. 

Physical Constitution of the Sun. 

Arctic Discovery. 

Spectrum Analysis. 

The late Eclipse of the Sun. 

The Forms and Action of Water. 

Organic Chemistry. 

The Chemistry of the Galvanic Bal 
tery considered in relation to 
Dynamics. 

The Balloon Ascents made for the 
British Association. 

The Chemical Action of Light. 

Recent Travels in Africa. 

Probabilities as to the position and 
extent of the Coal-measures be- 
neath the red rocks of the Mid- 
land Counties. 

The results of Spectrum Analysis 
applied to Heavenly Bodies. 

Insular Floras. 



LIST OF EVENING LECTDBES. 



lis 



Date and Place 



1867. Dundee. 



1868. Norwich ... 

1869. Exeter 

1870. Liverpool... 

1871. Edinburgh 

1872. Brighton ... 

1873. Bradford ... 

1874. Belfast 



1876. Bristol 



1876. Glasgow ... 



1877. Plymouth . 



1878. Dublin 



1879. Sheffield ... 

1880. Swansea ... 



1881. York. 



1882. Southamp- 

ton. 

1883. Southport 



1884. Montreal... 



1885. Aberdeen.. 



Lecturer 



Archibald Geikie, F.R.S 

Alexander Herschel, F.R.A.S. 

J. Fergiisson, F.E.S 

Dr. W. Odling, F.R.S 

Prof. J. Phillips, LL.D.,F.E.S. 
J. Norman Lockyer, F.R.S.... 

Prof. J. Tyndall, LL.D., F.R.S. 
Prof .W. J. Macquorn Eankine, 

LL.D., F.R.S. 
F. A. Abel, F.R.S 



E. B. Tylor, F.R.S 

Prof. P.Martin Duncan, M.B., 

TCI T> Q 

Prof. W.K. Clifford 



Subject of Discourse 



Prof. W. C.Williamson, F.R.S. 
Prof. Clerk Maxwell, F.R.S. 
Sir John Lubbock,Bart.,M.P., 

F.R.S. 
Prof. Huxley, F.R.S 

■W.Spottiswoode,LL.D.,F.R.S. 

F. J. Bramwell, F.R.S 

Prof. Tait, F.R.S.E 

SirAVyville Thomson, F.R.S. 
W. Warington Smyth, M.A., 

F.R.S. 

Prof. Odling, F.R.S 

G. J. Romanes, F.L.S 

Prof. Dewar, F.R.S 

W. Crookes, F.R.S 

Prof. E. Ray Lankester, F.R.S. 
Prof. W. Boyd Dawkins, 
F.R.S. 

Francis Galton, F.R.S 

Prof. Huxley, Sec. R.S 

W. Spottiswoode, Press. R.S. 

Prof. Sir Wm. Thomson, F.R.S. 
Prof. H. N. Moseley, F.R.S. 
Prof. R. S. Ball, F.R.S 

Prof. J. G. McKendrick, 
F.R.S.E. 

Prof. O. J. Lodge, D.Sc 

Rev. W. H. DaUinger, F.R.S. 



Prof. W. G. Adams, F.R.S. .., 
John Murray, F.R.S.E 



The Geological Origin of the present 
Scenery of Scotland. 

The present state of knowledge re- 
garding Meteors and Meteorites. 

Archeology of the early Buddhist 
Monuments. 

Reverse Chemical Actions. 

Vesuvius. 

The Physical Constitution of the 
Stars and Nebulse. 

The Scientific Useof the Imagination. 

Stream-lines and Waves, in connec- 
tion with Naval Architecture. 

Some recent investigations and ap- 
plications of Explosive Agents. 

The Relation of Primitive to Modern 
Civilization. 

Insect Metamorphosis. 

The Aims and Instruments of Scien- 
tific Thouglit. 

Coal and Coal Plants. 

Molecules. 

Common Wild Flowers considered 
in relation to Insects. 

The Hypothesis that Animals are 
Automata, and its History. 

Tlie Colours of Polarized Light. 

Railway Safety Appliances. 

Force. 

The Cliallfngcr Expedition. 

The Physical Phenomena connected 
with the Mines of Cornwall and 
Devon. 

The new Element, Gallium. 

Animal Intelligence. 

Dissociation, or Modern Ideas of 
Chemical Action. 

Radiant Matter. 

Degeneration. 

Primeval Man. 

Mental Imagery. 

The Rise and Progress of Palason* 

tology. 
The Electric Discharge, its Forms 

and its Functions. 
Tides. 

Pelagic Life. 
Recent Researches on the Distance 

of the Sun. 
Galvani and Animal Electricity. 

Dust. 

The Modern Microscope in Re- 
searches on the Least and Lowest 
Forms of Life. 

The Electric Light and Atmospheric 
Absorption. 

The Great Ocean Basins. 



Ix 



REPORT — 1885. 



LECTURES TO THE OPERATIVE CLASSES. 



Date and Place 


Lecturer 


Subject of Discourse 


1867. Dundee 


Prof. J. Tyndall, LL.D.,F.K.S. 


Matter and Force. 


1868. Norwich ... 


Prof. Huxley, LL.D., F.E.S. 


A Piece of Chalk. 


1869. Exeter 


Prof. Miller, M.D., F.E.S. ... 


Experimental illustrations of the 
modes of detecting the Composi- 
tion of the Sun and other Heavenly 
Bodies by the Spectrum. 


1870. Liverpool... 


Sir John Lubbock, Bart.,M.P., 
F.K.S. 


Savages. 


1872. Brighton ... 


W.Spottiswoode,LL.D.,F.R.S. 


Sunshine, Sea, and Sky. 


1873. Bradford ... 


C. W. Siemens, D.C.L., F.R.S. 


Fuel. 


1 874 Belfast 


Prof Odlino-. F.R.S 


The Discovery of Oxygen, 
A Piece of Limestone. 


X O 1 ^ t -^ v7 i. J. CuO Li ■•((•* 

1875. Bristol 


Dr. W. B. Carpenter, F.R.S. 


1876. Glasgow ... 


Commander Cameron, C.B., 

R.N. 
W. H. Preece 


A Journey through Africa. 


1877. Plymouth... 
1879 Sheffield 


Telegraphy and the Telephone. 
Electricity as a Motive Power. 
The North-East Passage. 


W E Avrton 


1880. Swansea ... 


H. Seebohm, F.Z.S 


1881. York 


Prof. Osborne Reynolds, 


Raindrops, Hailstones, and Snow- 




F.R.S. 


flakes. 


1882. Southamp- 


John Evans, D.C.L. Treas. R.S. 


Unwritten History, and how to 


ton. 




read it. 


1883. Southport 


Sir F. J. Bramwell, F.R.S. ... 


Talking by Electricity — Telephones. 


1884. Montreal ... 


Prof. R.S. Ball, F.R.S 


Comets. 


1885. Aberdeen... 


H. B. Dixon, M.A 


The Nature of Explosions. 



Ixi 



OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE. 

ABERDEEN MEETING. 

SECTION A. — MATHEMATICAL AND PHYSICAL SCIENCE. 

Fresiclent.—FToiessor G. Chrystal, M.A., F.R.S.E. 

Vice-Presidents.— ProkssoT C. Niven, F.R.S. ; Lord Rayleigh, F.R.S. ;. 
Professor A. Schuster, F.R.S. ; Professor G, G. Stokes, Sec.R.S. ; 
Professor Sir W. Thomson, F.R.S. 

Secretaries— R. E. Baynes, M.A. ; R. T. Glazebrook, F.R.S. ; Professor 
W. M. Hicks, F.R.S. (Becorder) ; Professor W. Ingram, M.A. 

SECTION B. — CHEMICAL SCIENCE. 

President.— Proiessov H. E. Armstrong, Ph.D., F.R.S., Sec.C.S. 

Vice-Presidents. — Professor Brazier, F.C.S. ; Professor A. Crum Brown, 
F.R.S. ; Professor Hartley, F.R.S. ; Professor H. McLeod, F.R.S. ; 
Professor W. A. Tilden, F.R.S. 

Secretaries. — Professor P. Phillips Bedson, D.Sc. {Becorder) ; H. B. 
Dixon, M.A. ; H. Forster Morley, D.Sc. ; W. J. Simpson, M.D. 

SECTION C. — GEOLOGY. 

PrmcZen^.— Professor J. W. Jndd, F.R.S., Sec.G.S. 

Vice-Presidents. — John Evans, Treas.R.S.; Rev. George Gordon, LL.D, ; 
T. F. Jamieson, LL.D. ; Rev. J. M. Joass, LL.D. ; Professor O. C. 
Marsh, M.A. ; Professor W. C. Williamson, F.R.S. 

Secretaries.— C. E. De Ranee, F.G.S. ; J. Home, F.R.S.E. ; J. J. H. 
Teall, F.G.S. ; W. Topley, F.G.S. {Recorder). 

SECTION D. — BIOLOGY. 

President.— PTo^esaov W. C. Mcintosh, M.D., LL.D., F.R.S. L. and E., 
F.L.S. 

Vice-Presidents. — Professor C. C. Babington, F.R.S. ; Professor I. Bayley 
Balfonr, F.R.S. ; Professor Cleland, F.R.S. ; Sir John Lubbock, 
Bart., F.R.S.; Professor J. S. Bnrdon Sanderson, F.R.S.; Pro- 
fessor W. Stirling, F.R.S.E. ; Professor Trail, F.L.S. 

Secretaries. — W. Heape ; J. McGi-egor- Robertson, M.B. ; J. Duncan 
Matthews, F.R.S.E. ; Howard Saunders, F.L.S. {Recorder) ; H.. 
Marshall Ward, M.A. 



Ixii REPORT — 1885. 

SECTION E. — GEOGRAPHY. 

Fresident.— General J. T. Walker, C.B., R.E., LL.D., F.R.S. 

Vice-Presidents. — Professor James Donaldson, F.R.S.E. ; Admiral Sir E. 
Ommanney, C.B,, F.R.S. ; Lieat.- Colonel R. L. Playfair; Dr. John 
Rae, F.R.S. 

Secretaries.— J. S. Keltie ; J. S. O'Halloran, F.R.G.S.; E. G. Raven- 
stein, F.R.G.S. (Recorder) ; Rev. G. A. Smith, M.A. 

SECTION F. — ECONOMIC SCIENCE AND STATISTICS. 

President. — Professor Henry Sidgwick, LL.D., Litt.D. 

Vice-Presidents. — Professor Adanison, LL.D. ; Dr. Alexander Bain ; 
Major P. G. Craigie ; Sir Richard Temple, Bart., G.C.S.I. 

.Secretaries. — Rev. W. Cunningham, B.D. ; Professor H. S. Foxwell, 
M.A. (Recorder) ; C. McCombie ; J. F. Moss. 

SECTION G. — MECHANICAL SCIENCE. 

President. — Benjamin Baker, M.Inst. C.E. 

Vice-Presidents. — W. H. Barlow, F.R.S. ; Sir James N. Douglass ; Pro- 
fessor James Thomson, F.R.S. ; Professor W. C. Unvvin. 

■Secretaries. — A. T. Atchison, M.A. ; F. G. Ogilvie, M.A., B.Sc. ; E. 
Rigg, M.A. (Recorder) ; J. N. Shoolbred, B.A. 

SECTION H. — ANTHROPOLOGY. 

President. — Francis Galton, M.A., F.R.S., President of the Anthropo- 
logical Institute. 

Vice-Presidents. — Dr. Alexander Bain ; Professor D. J. Cunningham, 
M.D. ; Professor Flower, F.R.S. ; W. Pengelly, F.R.S. ; Professor 
Strnthers, M.D. ; Professor W. Turner, F.R.S. 

.Secretaries. — G. W. Bloxam, F.L.S. (Recorder) ; J. G. Garson, M.D. ; 
Walter Hurst, B.Sc. ; A. McGregor, M.D. 







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Ixiv 



EEPORT — 1885. 

Ta^le showing the AttendaTice and ReceipU 



Date of Meeting 



1831, Sept. 27 .. 

1832, June 19 .. 

1833, June 25 .. 

1834, Sept. 8 .. 

1835, Aug. 10 .. 

1836, Aug. 22 .. 

1837, Sept. 11 .. 

1838, Aug. 10 .. 
183!), Aug. 26 .., 

1840, Sept. 17 .. 

1841, July 20 .. 

1842, June 23 .. 

1843, Aug. 17 .. 

1844, Sept. 26 .. 

1845, June 19 .. 

1846, Sept. 10 .. 

1847, June 23 .. 

1848, Aug. 9 .. 

1849, Sept. 12 .. 

1850, July 21 .. 

1851, July 2 .. 

1852, Sept. 1 .. 

1853, Sept. 3 .. 

1854, Sept. 20 .. 

1855, Sept. 12 .. 

1856, Aug. 6 .. 

1857, Aug. 26 .. 

1858, Sept. 22 .. 

1859, Sept. 14 .. 

1860, June 27 .. 

1861, Sept. 4 .. 

1862, Oct. 1 .. 

1863, Aug. 26 .. 

1864, Sept. 13 .. 

1865, Sept. 6 .. 

1866, Aug. 22 .. 

1867, Sept. 4 .. 

1868, Aug. 19 .. 

1869, Aug. 18 .. 

1870, Sept. 14 .. 

1871, Aug. 2 ., 

1872, Aug. 14 .. 

1873, Sept. 17 ., 

1874, Aug. 19 . 

1875, Aug. 25 . 

1876, Sept. 6 . 

1877, Aug. 15 . 

1878, Aug. 14 . 

1879, Aug. 20 . 

1880, Aug. 25 . 

1881, Aug. 31 . 
] 882, Aug. 23 . 

1883, Sept. 19 ., 

1884, Aug. 27 . 

1885, Sept. 9 . 



Where held 



Presidents 



York 

Oxford 

Cambridge 

Edinburgh 

Dublin 

Bristol 

Liverpool 

Newcastle-on-Tyne 

B irmingham 

Glasgow 

PljTnoiith 

Manchester 

Cork 

York 

Cambridge 

Southamijton 

Oxford 

Swansea 

Birmingham 

Edinburgh 

Ipswich 

Belfast 

Hull 

Liverpool 



Glasgow 

Cheltenham 

Dublin 

Leeds 

Aberdeen 

Oxford 

Manchester 

Cambridge 

Newcastle-on-Tyne 

Bath 

Birmingham 

Nottingham 

Dundee 

Norwich 

Exeter 

Liverpool 

Edinburgh 

Brighton 

Bradford 

! Belfast 

! Bristol 

Glasgow 

Plymouth 

Dublin 

Sheffield 

Swansea 

York 

Southampton 

Southport 

Montreal 

Aberdeen 



The Earl Fitzwilliam, D.C.L. 
The Rev. W. Buckland, F.R.S. 
The Rev. A. Sedgwick, F.R.S. 

Sir T. M. Brisbane, D.C.L 

The Rev. Provost Lloyd, LL.D. 
The Marquis of Lansdowne ... 
The Earl of Burlington, F.R.S. 
The Duke of Northumberland 
The Rev. W. Vernon Harcourt 
The Marquis of Breadalbane... 
The Rev. W. WnevfeU, F.R.S. 

The Lord Francis Egertou 

The Earl of Rosse, F.R.S 

The Rev. G. Peacock, D.D. ... 
Sir John F. W. Herschel, Bart. 
Sir Roderick I. i\Iurchison,Bart. 

Sir Robert H. Inglia, Bart 

The Marquis of Northampton 
The Rev. T. R. Robinson, D.D. 

Sir David Brewster, K.H 

G. B. Airy, Astronomer Royal 
Lieut.-General Saljine, F.R.S. 

William Hopkins, F.R.S 

The Earl of Harrowby, F.R.S. 

The Duke of Arayll, F.R.S. ... 

Prof. C. G. B. Daubeny, M.D. 

The Rev.Humphiev Lloyd, D.D. 

Richard Owen, M'D., D.C.L.... 

H.R.H. the Prince Consort ... 

I The Lord Wrottesley, M.A. .. 

WilliamFairbaim,LL.D.,F.R.S. 

I The Rev. Prof essor Willis, M.A. 

Sir William G.Armstrong, C.B. 

Sir Charles Lyell, Bart., M.A. 

1 Prof. J. Phillips, M.A., LL.D. 

I William R. Grove, Q.C., F.R.S. 

I The Duke of Buccleuch,K.C.B. 

1 Dr. Joseph D. Hooker, F.R.S. 

i Prof. G. G. Stokes, D.C.L 

Prof. T. H. Huxley, LL.D 

Prof. Sir W. Thomson, LL.D. 

Dr. W. B. Carpenter, F.R.S. ... 

Prof. A. W. Williamson, F.R.S. 

Prof. J. Tyndall, LL.D., F.R.S. 

SirJohnHawkshaw,C.E.,F.R.S. 

Prof. T. Andrews, M.D., F.R.S. 

Prof. A. Thomson, M.D., F.R.S. 

W. Spottiswoode, M.A., F.R.S. 

Prof.G. J. Allman, M.D., F.R.S. 

A. C. Ramsay, LL.D., F.R.S.... 

Sir John Lubbock, Bart., F.R.S. 

Dr. C. W. Siemens, F.R.S 

Prof. A. Cayley, D.C.L., F.R.S. 

Prof. Lord Rayleigh, F.R.S. ... 

Sir Lyon Playf air, K.C.B.,F.E.S. 



Old Life 
Members 



169 

303 

109 

226 

313 

241 

314 

149 

227 

235 

172 

164 

141 

238 

194 

182 

236 

222 

184 

286 

321 

239 

203 

287 

292 

207 

167 

196 

204 

314 

246 

245 

212 

162 

239 

221 

173 

201 

184 

144 

272 

178 

203 

235 

225 



ATTENDANCE AND RECEIPTS AT ANNUAL MEETINGS. 



Ixv 



Innual Meetings of the Association. 



Attended by 


Amount 


Sums paid on 

Account of 

Grants for 

Scientific 

Purposes 




Old 

anual 

mbers 


New 

Annual 

Members 


Asso- 
ciates 


Ladies 


For- 
eigners 


Total 


received 

during the 

Meeting 


Year 


... 




... 


... 


353 






1831 
1832 










... 


... 






... 


... 


900 
1298 






1833 
18.34 
1835 




£20 
167 




••• 


... 






lioo* 


... 


1350 
1840 
2400 




435 

922 12 6 
932 2 2 


1836 
1837 
1838 






46 


ill 

376 
185 
190 
22 
39 
40 
25 






"eo* 

331* 

160 

260 

172 

196 

203 

197 


34 

40 

28 

35 
36 
53 
15 


1438 

1353 

891 

1315 

1079 

857 

1320 

819 




1595 11 

1546 16 4 

1235 10 11 

1449 17 8 

1565 10 2 

981 12 8 

831 9 9 

685 16 

208 5 4 

275 1 8 


1839 
1840 
1841 
1842 
1843 
1844 
1845 
1846 
1847 
1848 






75 


'33t 

'"at 

407 
270 
495 
376 





71 




45 




94 




65 




197 




54 


£m"6'o 


93 


33 


447 


237 


22 


1071 


963 


159 19 6 


1849 


128 


42 


510 


273 


44 


1241 


1085 


345 18 


1850 


61 


47 


244 


141 


37 


710 


620 


391 9 7 


1851 


63 


60 


510 


292 


9 


1108 


1085 


304 6 7 


1852 


56 


57 


367 


236 


6 


876 


903 


205 


1853 


121 


121 


76.5 


524 


10 


1802 


1882 


380 19 7 


1854 


142 


101 


1094 


543 


26 


2133 


2311 


480 16 4 


1855 


104 


48 


412 


346 


9 


1115 


1098 


734 13 9 


1856 


156 


120 


900 


569 


26 


2022 


2015 


507 15 4 


1857 


111 


91 


710 


509 


13 


1698 


1931 


618 18 2 


1858 


125 


179 


1206 


821 


22 


2564 


2782 


684 11 1 


1859 


177 


59 


636 


463 


47 


1689 


1604 


766 19 6 


1860 


184 


125 


1589 


791 


15 


3138 


3944 


1111 5 10 


1861 


150 


57 


433 


242 


25 


1161 


1089 


1293 16 6 


1862 


154 


209 


1704 


1004 


25 


3335 


3640 


1608 3 10 


1863 


182 


103 


1119 


1058 


13 


2802 


2965 


1289 15 8 


1864 


215 


149 


766 


508 


23 


1997 


2227 


1591 7 10 


1865 


J18 


105 


960 


771 


11 


2303 


2469 


1750 13 4 


1866 


193 


118 


1163 


771 


7 


2444 


2613 


1739 4 


1867 


J26 


117 


720 


682 


45| 


2004 


2042 


1940 


1868 


229 


107 


678 


600 


17 


1856 


1931 


1622 


1869 


503 


195 


1103 


910 


14 


2878 


3096 


1572 


1870 


511 


127 


976 


754 


21 


2463 


2575 


1472 2 6 


1871 


280 


80 


937 


912 


43 


2533 


2649 


1285 


1872 


237 


99 


796 


601 


11 


1983 


2120 


1685 


1873 


532 


85 


817 


630 


12 


1951 


1979 


1151 16 


1874 


307 


93 


884 


672 


17 


2248 


2397 


960 


1875 


531 


185 


1265 


712 


25 


2774 


3023 


1092 4 2 


1876 


238 


59 


446 


283 


11 


1229 


1268 


1128 9 7 


1877 


290 


93 


1285 


674 


17 


2578 


2615 


725 16 6 


1878 


239 


74 


629 


349 


13 


1404 


1425 


1080 11 11 


1879 


171 


41 


889 


147 


12 


915 


899 


731 7 7 


1880 


U13 


176 


1230 


514 


24 


2557 


2689 


476 3 1 


1881 


253 


79 


516 


189 


21 


1253 


1286 


1126 1 11 


1882 


!30 


323 


952 


841 


5 


2714 


3369 


1083 3 3 


1883 


517 


219 


826 


74 


26&60H.§ 


1777 


1538 


1173 4 


1884 


532 


122 


1053 


447 


6 


2203 


2256 


1385 


1885 



dies were not admitted ty purchased Tickets until 1843. + Tickets of Admission to Sections only, 

cludmg Ladies. § Fellows of the American Association wer» admitted as Honorary Members for this Meeting 

d 



OFFICERS AND COUNCIL, 1885-86. 



PRESIDENT. 
The Right Hon. SIR LYON PLATFAIR, K.C.B., M.P., Ph.D., LL.D., F.R.S.L.&E., F.C.S. 

VICE-PRESIDENTS. 

His Grace the Duke o£ Richmond and Gordon, K.G., D.C.L., Cliaucellor of tlie 

University of Aberdeen. 

Tlie Right Hon. the Earl of Aberdeen, LL.D., Lord-Lieutenant of Aberdeenshire. 

The Right Hon. the Earl of Crawkord and Balcarres, M.A., LL.D., F.R.S., F.R.A.S. 

James Matthews, Esq., Lord Provost of the City of Aberdeen. 

Professor Sir William Thomson, M.A., LL.D., F.R.S. L. & E., F.R.A.S. 

Alexander B.un, Esq., M.A., LL.D.. Rector of the University of Aberdeen. 

Professor W. H. Flower, LL.D., F.R.S., F.L.S., F.G.S., Pres. Z.S., Director of 

the Natural History Museum, London. 

Professor John Struthers, M.D., LL.D. 

PRESIDENT ELECT. 

Sir William Dawson, C.M.G., JI.A.. LL.D., F.R.S. , P.G.S., Principal of McGill College, Montreal, Canada. 



VICE-PRESID 

The Right Hon. the Earl op Bradford, Lord- 
Lieutenant of Shropsliire. 

The Riglit Hon. Lord Leioh, D.C.L., Lord-Lieu- 
tenant of Warwicksiiire. 

The Bight Hon. LoiiD Norton, K.C.M.G. 

The Right Hon. Loud Wrottesley, Lord-Lieu- 
tenant of Staffordshire. 



ENTS ELECT. 

The Riglit Rev. the Lord Bishop of Worcester, 

D.D. 
THOJU.S Martineau, Esq., Mayor of Birmingham. 
Professor G. G. Stokes, D.C.L., LL.D., Pres. R.S. 
Professor W. A. Tilden, D.Sc, F.R.S., F.C.S. 
Rev. A. R. Vardy, M.A. 
Rev. A. W. Watson, D.Sc, F.R.S. 



LOCAL SECRETARIES FOR THE MEETING AT BIRMINGHAM. 
J. Barh-UI Carslake, Esq. | Rev. H. W. Crosskey, LL.D., F.G.S. | Charles J. Hart, Esq. 

LOCAL TREASURER FOR THE MEETING AT BIRMINGHAM. 
J. D. Goodman, Esq. 



ORDINARY MEMBERS 
Abney. Capt. W. DE W., F.R.S. 
Ball, Professor R. S., F.R.S. 
Bateman, J. F. La Trobe. Esq., F.R.S. 
BL.4.NF0RD, W. T., Esq., F.R.S. 
Bramwell, Sir F. J.. F.R.S. 
Crookes, W., Esq., F.R.S. 
Dawkins, Professor W. Boyn, F.R.S. 
De La Rue, Dr. Warren, F.R.S. 
Dewar, Professor J., F.R.S. 
Flower, Professor W. H., F.R.S. 
Gl.\dstoxe, Dr. J. H., F.R.S. 
Gl.u.sheb, J. W. L., Esq., F.R.S. 
God WIN- Austen, Lieut.-Col. H. H., F.R.S. 



OF THE COUNCIL. 

Hawkshaw, J. Clarke, Esq., F.G.S. 
Hknrici, Professor 0., F.R.S. 
Hughes, Professor T. McK., F.G.S. 
Martin, J. B., Esq.. F.S.S. 
M'Leod, Professor H., F.R.S. 
MosKLEV. Professor H. N., F.R.S. 
Ojimanxey, Admiral Sir E., C.B., F.R.S. 
Pengelly, W., Esq., F.R.S. 
Perkin, Dr. W. H., F.R.S. 
SORBY, Dr. H. C. F.R.S. 
Temple, Sir R., Bart. G.C.S.I. 
Thiselton-Dyer, W. T., Esq., C.M.G., 
F.B.S. 



GENERAL SECRETARIES. 

Capt. Douglas Galton, C.B., D.C.L., LL.D., F.R.S., F.G.S., 12 Chester Street, London, S.\7. 

A. G. Vernon Harcourt, Esq., M.A., LL.D., F.R.S., F.C.S., Cowley Grange. Oxford. 

SECRETARY. 
Arthur T. Atchison, Esq., M.A., 22 Albemarle Street, London, W. 

GENERAL TREASURER. 
Professor A. W. Williamson, Ph.D., LL.D., F.R.S., F.C.S., University College, London, W.C. 

EX-OFFICIO MEMBERS OF THE COUNCIL. 
The Trustees, the President and President Elect, tlie Presiilents of former years, the Vice-Presidents and 
Vice-Presidents Elect, the General and Assistant General Secretaries for the present and former yeai-s, 
the Secretary, the Genpral Treasurers for the present and former years, and the Local Treasurer and 
Secretaries for the eusuuig Meeting. 

TRUSTEES (PERMANENT). 
Sir John Lubbock, Bart.. MP., D.C.L., LL.D., F.R.S., Pres. L.S. 
The Right Hon. Lord Rayleigh, M.A., D.C.L., LL.D., Sec. R.S., F.R.A.S. 
The Right Hon. Sir Lyon Playfair, K.C.B., M.P., Ph.D., LL.D., F.R.S. 



PRESIDENTS OF FORMER TEARS. 



The Duke of Devonshire, K.G. 
Sir G. B. Airy, K.C.B., F.R.S. 
The Duke of Argyll, K.G., K.T. 
Sir Richard Owen, K.C.B., F.R.S. 
Sir W. G. Armstrong, C.B., LL.D. 
Sir William R. Grove, F.R.S. 



Sir Joseph D. Hooker, K.C.S.I. 
Prof. Stokes, D.C.L., Pres. R.S. 
Prof. Huxley, LL.D., F.R.S. 
Prof. Sir Wm. Tliomson, LL.D. 
Prof. Williamson, Ph.D., F.R.S. 
Prof. Tvndall, D.C.L., F.R.S. 



Sir John Hawkshaw, F.R.S. 
Prof. AUman, M.D., F.R.S. 
Su- A. C. Ramsay, LL.D., F.R.S. 
Sir John Lubbock, Bart., F.R.S. 
Prof, Cayley, LL.D., F.R.S. 
Lord Rayleigh, D.C.L., Sec. R.S. 



P. Galton. Esq., F.R.S. 
Dr.T. A. Hirst, F.R.S. 



GENERAL OFFICERS OP FORMER TEARS. 

I Dr. Michael Foster, Sec. R.S. | P. L. Sclater, Esq., Ph.p.,_P.R.S. , 



GeorgeGriffith, Esq., M.A,, F.C.S. I Prof. Bonney, D.Sc, F.R.S. 



John Evans, Esq., D.C.L., F.R.S. 



AUDITORS. 
I W. Huggins, Esq., D.C.L., 



F.R.S. I W. H. Preece, Esq., F.R.S. 



Ixvii 



REPORT OF THE COUNCIL. 

Heport of the Council for the year 1884-85, presented to the General 
Committee at Aberdeen, on Wednesday, September 9, 1885. 

The Council have received reports during the past year from the 
Oeneral Treasurer, and his accounts for the year will be laid before the 
General Committee this day. 

Since the Meeting at Montreal, the following have been elected 
Corresponding Members of the Association : — 

Bowditch, Prof. H. P. Kikuchi, Prof. Dairoku. 

Brusb, Prof. G. J. Michelson, A. A. 

Gibbs, Prof. J. Willard. Newcomb, Prof. Simon. 

Gibbs, Prof. Wolcott. Powell, Major J. W. 

Greely, Lieut. A. W. Ray, Captain P. H. 

Jackson, Prof. C. Loring. Thurston, Prof. R. H. 

The Council have nominated Professor Struthers, M.D., LL.D., to 
he a Vice-President at the Meeting at Aberdeen. 

Soon after the commencement of the present year, Professor Bonney, 
-the Secretary, informed the Council that a considerable increase in the 
endowment of his Professorship at University College would demand 
that in future a larger share of his time should be devoted to teaching. 
As unfortunately the state of his health for some months past had pointed 
to the need of diminishing rather than increasing his work, he regretted 
that he would be unable to offer himself for re-election at the present 
Meeting. The Council received this announcement with very great 
regret." Professor Bonney not only brought to the office of Secretary a 
leading scientific position, but also combined with this advantage great 
energy, zeal, and discretion. It was largely due to his powers of organi- 
sation and tact that the exceptional and grave difficulties which attended 
the holding of last year's Meeting at Montreal were surmounted, and it 
was brought to a successful issue. The Council have nominated Mr. A. T. 
Atchison M.A., who for some years past has rendered most efficient 
assistance as one of the Secretaries of Section G, to the office of Secretary, 
vacated by Professor Bonney. 

During the present year the Council have considered the stipend 
paid to Mr. Stewardson, the Clerk of the Association, and the amount 
assigned to the General Treasurer to enable him to obtain such assistance 
as may be requisite. Mr. Stewardson was engaged in the year 1873 at a 
salary of 120Z., which was subsequently augmented to VSOl. The Council 
now recommend that for the present year it be raised to 135Z., and be 
subsequently increased (subject to the usual conditions) by a sum of 51. at 
the end of each three years till a maximum of 160L be reached ; also that 
the yearly sum assigned to the General Treasurer be increased from 501. 

to 601. 

d 2 



Ixviii KEPORT — 1885. 

On meeting again in Great Britain, the Council venture to express 
to the General Committee their belief that the anticipations of a successful 
meeting, expressed in the Report presented at Montreal, have been fully 
justified by the results, and once more give utterance to the gratitude, 
which must be felt by all who visited Canada, for the liberal hospitality 
and cordial reception which welcomed them there. It will be long before 
this visit is forgotten, or the stimulus, which its exceptional circumstances 
gave to the energy and life of the Association, ceases to be felt. Towards 
the close of that Meeting the happy idea occurred to several members of 
the Association that it would be an appropriate memorial of the visit 
of the British Association to found a Medal at McGill University, to be 
given annually for proficiency in Applied Science. The idea, once started, 
was warmly espoused, and a subscription list was opened, with Lord 
Rayleigh, the President, as Treasurer, and Messrs. W. Topley and H. T. 
Wood as Secretaries. The result has been that a sum of about 5001. 
will be transmitted to the authorities of the McGill University for invest- 
ment. This will enable them to offer, as an annual prize, a Gold Medal 
and a sum of money. The first award has already been made. The 
Council, acting under the powers conferred upon them by the General 
Committee on Nov. 11, 1884, have instructed Mr. Wyon to prepare, at 
the cost of the Association, a suitable die for the Medal. 

The Council, in virtue of the powers conferred upon them by the 
General Committee at Montreal, in regard to the report concerning 
Corresponding Societies, have formed the Corresponding Societies' 
Committee. The Report of the Committee will be presented, and a con- 
ference of Delegates, appointed under the new rules, will be held during 
the present meeting. 

The following resolutions were referred by the General Committee to 
the Council for consideration and action, if desirable : — 

' That the Council of the Association be requested to communicate 
with the Government of the Dominion of Canada in order (1) to call 
the attention of the Government to the absence of trustworthy informa- 
tion concerning the tides of the Gulf of St. Lawrence and the adjoining 
Atlantic coast, and to the dangers which thence arise to the navigation ; 
(2) To urge upon the Government the importance of obtaining accurate 
and systematic tidal observations, and of tabulating and reducing the 
results by the scientific methods elaborated by Committees of the Associa- 
tion ; and (3) to suggest the immediate establishment of a sufficient 
eeries of observing stations on the coast of the Dominion.' 

A memorial in accordance with the above resolution was adopted 
by the Council and forwarded to the Government of the Dominion of 
Canada. To this a reply was received from the Canadian Minister of 
Marine, expressing regret that the Dominion Government were unable 
at the present time to undertake a special sui'vey of the tides and currents 
in the Gulf of St. Lawrence. The Council, however, are not without 
hope that the proposed observations may be regarded as deferred rather 
than as refused. 

' That the Council memorialise the Canadian Government as to the 
urgent necessity of encouraging investigation and publication of reports 
with respect to the physical characters, languages, social, industrial, and 
artistic condition of the native tribes of the Dominion.' 

A memorial in accordance with the above was also adopted by the 
■Council and forwarded to the Government of the Dominion of Canada. 



REPORT OF THE COUNCIL. Ixix 

The receipt of this was acknowledged, and the Conncil were informed 
that it would be duly considered by the Dominion Government. 

' That the attention of the Council be drawn to the advisability of 
communicating with the Admiralty for the purpose of urging on them 
the importance of the employment of the Harmonic Analysis in the 
Reduction of Admiralty Tidal Observations.' 

The above recommendation was duly considered, but the Council, 
while fully conscious of the importance of the subject, deemed the time 
inopportune for pressing the matter on the attention of the Admiralty. 

' That the Council be requested to examine the feasibility of insti- 
tuting a scheme for pi'omoting an International Scientific Congress, to meet 
at intervals in different countries, and to report thereon to the General 
Committee at the next meeting of the Association.' 

This most important question has been very fully considered by the 
Council during the past year. The importance of such a Congress can 
hardly be doubted ; at the same time there are many serious difficulties in 
devising a practical scheme, and many considerations to be taken into 
account, before it would be prudent to undertake so great a departure 
from the ordinary procedure of the Association, as would be involved by 
such schemes as have seemed most feasible. The following is a brief 
history of what has been done : At the conclusion of the Montreal Meeting 
a Committee of the Council (of which Mr. Vernon Harcourt, the General 
Secretary, was a member) took the opportunity of being present at the 
meeting of the American Association at Philadelphia to confer with some 
members of the Committee in America, from whom the latest and most 
definite proposal of an International Scientific Association has emanated. 
After returning to England, a letter was received by Mr. Vernon Harcourt 
from Dr. S. C. Minot, Secretary to the above Committee, which was laid 
before a Committee of the Council. As a result of their consideration of 
this letter, the Secretary entered into an informal correspondence with 
Dr. C. S. Minot. The intent of this correspondence was to bring about 
an exchange of views and a discussion of certain difficulties which pre- 
sented themselves at first sight, and as it, in effect, contains the outline of 
a scheme, the Council (with Dr. Minot's permission) have resolved to place 
it, together with extracts from his letter to Mr. Vernon Harcourt, in the 
hands of the General Committee. Copies of it are accordingly distributed 
with this Report. The Council, in the next place, deemed it desirable to 
ascertain what support the proposal of a joint meeting of the British 
Association and of the International Scientific Association, in the suggested 
rudimentary form, would meet with from the more important scientific 
societies in London ; for, without their favourable countenance and the 
permission to use the rooms of such as were couveniently situated, the 
project would necessarily be abortive. A circular was accordingly ad- 
dressed to a number of the London scientific societies, with the result 
that out of 29 societies which sent answers, three expressed their inability, 
in consequence of formal difficulties, to reply at present ; two were 
opposed to the scheme ; five were favourable ; and the rest were not 
hostile. It should, however, be remarked, that while a willingness to 
lend rooms was very generally shown, any approbation of the scheme was 
expressed in very guarded terms, and amounted, in the majority of cases, 
to little more than a non-expression of disapproval. In these circum- 
stances the Council invite the General Committee to take the matter into 



Ixx 



REPORT — 1885. 



tlieir consideration duriDg the Aberdeen Meeting, and suggest that the 
second meeting of the General Committee would be the most convenient 
opportunity for a discussion. 

One vacancy in the Council has been caused by the lamented death 
of Dr. Gwyn Jeffreys ; another by the resignation of Prof. Prestwich ; it 
follows, therefore, that in accordance with the rule, three other members 
will retire. The retiring members will be : — 

Sir F. J. Evans. Prof. W. G. Adams. 

The Right Hon. G. Sclater-Booth. 

The Council recommend the re-election of the other ordinary Members 
of Council, with the addition of the gentlemen whose names are distin- 
guished by an asterisk in the following list : — 



Abney, Capt. W. de W., F.R.S. 
Ball, Prof. R. S., F.R.S. 
Bateman, J. F. La Trobe, Esq., 

F.R.S. 
*Blanford, W. T., Esq., F.R.S. 
Bramwell, Sir F. J., F.R.S. 
*Crookes, W., Esq., F.R.S. 
Dawkins, Prof. W. Boyd, F.R.S. 
De La Rue, Dr. Warren, F.R.S. 
Dewar, Prof. J., F.R.S. 
Flower, Prof. W. H., F.R.S. 
Gladstone, Dr. J. H., F.R.S. 
Glaisher, J. W. L., Esq., F.R.S. 
Godwin-Austen, Lieut.-Col. H. H., 

F.R.S. 



Hawkshaw, J. Clarke, Esq., F.G.S. 
Henrici, Prof. O., F.R.S. 
Hughes, Prof. T. McK., F.G.S. 
*Martin, J. B., Esq., F.S.S. 
*M'Leod, Prof. H., F.R.S. 
Moseley, Prof. H. N., F.R.S. 
Ommanney, Admiral Sir E., C.B., 

F.R.S. 
Pengelly, W., Esq., F.R.S. 
Perkin, Dr. W. H., F.R.S. 
Sorby, Dr. H. C, F.R.S. 
Temple, Sii- R., Bart., G.C.S.I. 
•Thiselton-Dyer, W. T., Esq.,. 

C.M.G., F.R.S. 



Ixxi 



Recommendations adopted by the General Committee at the 
Aberdeen Meeting in September 1885. 

[When Committees axe appointed, the Member first named is regarded as the 
Secretary, except there is a specific nomination.] 

Involving Grants of Money. 

That Professor G. Carey Foster, Sir William Thomson, Professor 
Ayrton, Professor J. Perry, Professor W. G. Adams, Lord Rayleigh, 
Dr. 0. J. Lodge, Dr. Johu Hopkinson, Dr. A. Muirhead, Mr. W. H. 
Preece, Mr. Herbert Taylor, Professor Everett, Professor Schuster, Dr. 
J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glazebrook, Professor 
Chrystal, Mr. H. Tomlinson, Professor W. Garnett, Professor J. J. 
Thomson, and Mr. TV". N. Shaw be reappointed a Committee for the 
purpose of constructing and issuing practical Standards for use in 
Electrical Measurements ; that Mr. Glazebrook be the Secretary, and 
that the sum of 40/. be placed at their disposal for the purpose. 

That Professor Balfour Stewart, Professor Schuster, Professor Stokes, 
Mr. G. Johnstone Stoney, Professor Sir H. E. Roscoe, Captain Abney, and 
Mr. G. J. Symons be reappointed a Committee for the purpose of con- 
sidering the best methods of recording the direct intensity of Solar Eadia- 
tion ; that Professor Balfour Stewart be the Secretary, and that the un- 
expended sum of 20Z. be placed at their disposal for the purpose. 

That Professor Balfour Stewart (Secretary), Mr. Knox Laughton, Mr. 
G. J. Symons, and Mr. R. H. Scott be reappointed a Committee, with 
power to add to their number, for the purpose of co-operating with Mr. 
E. J. Lowe in his project of establishing a Meteorological Observatory 
near Chepstow on a permanent and scientific basis, and that the unex- 
pended sum of 25Z. be again placed at their disposal for the purpose. 

That Professor G. H. Darwin, Sir W. Thomson, and Major Baird be 
a Committee for the purpose of preparing instructions for the practical 
work of Tidal Observation ; that Professor Darwin be the Secretary, 
and that the sum of oOl. be placed at their disposal for the purpose. 

That Professors Balfour Stewart and Sir W. Thomson, Sir J. H. 
Lefroy, Sir Frederick Evans, Professor G. H. Darwin, Professor G. 
Chrystal, Professor S. J. Perry, Mr. C. H. Carpmael, Professor Schuster, 
Mr. G. M. Whipple, and Captain Creake be reappointed a Committee for 
the purpose of considering the best means of comparing and reducing 
Magnetic Observations ; that Professor Balfour Stewart be the Secretary, 
and that the sum of 40Z. be placed at their disposal for the purpose. 

That Professor G. Forbes, Captain Abney, Dr. J. Hopkinson, 
Professor W. G. Adams, Professor G. C. Foster, Lord Rayleigh, Mr. 
Preece, Professor Schuster, Professor Dewar, Mr. A. Vernon Har- 
court. Professor Ayrton, and Sir James Douglass be reappointed a Com- 
mittee for the purpose of reporting on Standards of Light ; that Professor 
G. Forbes be the Secretary, and that the sum of 201. be placed at their 
disposal for the purpose. 



Ixxii EEPORT — 1885. 

That Professor Crura Brown, Mr. Milne-Home, Mr. John Murray, 
and Mr. Bnchan be reappointed a Committee for the purpose of co- 
operating with the Scottish Meteorological Society in making meteoro- 
logical observations on Ben Nevis ; that Professor Crum Brown be the 
Secretary, and that the sum of lOOZ. be placed at their disposal for the 
purpose. 

That Professors Armstrong, Lodge, and Sir William Thomson, Lord 
Rayleigh, Professors Schuster, Poynting, J. J. Thomson, Fitzgerald, Crum. 
Brown, Ramsay, Frankland, Tilden, and Hartlev, Captain Abney, Messrs. 
W. N. Shaw, H. B. Dixon, J. T. Bottomley, W. Crookes, and Shelford 
Bidwell, and Dr. Fleming be a Committee for the purpose of considering 
the subject of Electrolysis in its Physical and Chemical bearings ; that 
Professor Armstrong be the Chemical Secretary and Professor Lodge the 
Physical Secretary, and that the sum of 20Z. be placed at their disposal 
for the purpose. 

That Professors McLeod and Ramsay and Mr. W. A. Shenstone be a 
Committee for the further investigation of the Influence of the Silent 
Discharge of Electricity on Oxygen and other gases ; that Mr. W. A. 
Shenstone be the Secretary, and that the sum of 20Z. be placed at their 
disposal for the purpose. 

That Professors Williamson, Dewar, Frankland, Crum Brown, Odling, 
and Armstrong, Drs. Hugo Miiller, A. G. Vernon Harcourt, F. R. Japp, 
and H. Forster Morley, and ]\Iessrs. C. E. Groves, J. Millar Thomson, V. H. 
Veley, and H. B. Dixon be reappointed a Committee for the purpose of 
drawing up a statement of the varieties of Chemical Names which have 
come into use, for indicating the causes which have led to their adoption, 
and for considering what can be done to bring about some convergence 
of the views on Chemical Nomenclature obtaining among English and 
foreign chemists ; that Mr. H. B. Dixon be the Secretary, and that the 
sum of bl. be placed at their disposal for the purpose. 

That Mr. W. T. Blanford, Professor J. W. Judd, and Messrs. W. Car- 
ruthers, H. Woodward, and J. S. Gardner be reappointed a Committee 
for the purpose of reporting on the Fossil Plants of the Tertiary and 
Secondary Beds of the United Kingdom ; that Mr. J. S. Gardner be the 
Secretary, and that the sum of 20L be placed at their disposal for the 
purpose. 

That Professor T. McK. Hughes, Dr. H. Hicks, Dr. H. Woodward, 
and Messrs. E. B. Luxmoore, P. Pennant, and Edwin Morgan be a Com- 
mittee for the purpose of exploring the Caves of North Wales ; that 
Dr. H. Hicks be the Secretary, and that the sum of 251. be placed at 
their disposal for the purpose. 

That Mr. R. Etheridge, Mr. T. Gray, and Professor John Milne be 
reappointed a Committee for the purpose of investigating the Volcanic 
Phenomena of Japan ; that Professor John Milne be the Secretary, and 
that the sum of 501. be placed at their disposal for the purpose. 

That Messrs. R. B. Grantham, C. E. De Ranee, J. B. Redman, W. 
Topley, W. Whitaker, and J. W. Woodall, Major-General Sir A. Clarke, 
Admiral Sir E. Ommanney, Sir J. N. Douglass, Captain Sir F. J. O. 
Evans, Captain J. Parsons, Captain W. J. L. Wharton, Professor J. 
Prestwich, and Messrs. E. Fasten, J. S. Valentine, and L. F. Vernou 
Harcourt be reappointed a Committee for the purpose of inquiring into 
the Rate of Erosion of the Sea-coasts of England and Wales, and the 
Influence of the Artificial Abstraction of Shingle or other Material in that 



RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxiii 

Action ; that Messrs. De Ranee and Topley be tlie Secretaries, and that 
the sum of 20?. be placed at their disposal for the purpose. 

That Messrs. H. Bauerman, F. W. Rndler, J. J. H. Teall, and H. J. 
Johnston-Lavis be reappointed a Committee for the purpose of investi- 
gating the Volcanic Phenomena of Vesuvius and its neighbourhood ; that 
Mr. H. J. Johnston-Lavis be the Secretary, and that the sum of 30?. be 
placed at their disposal for the purpose. 

That Dr. J. Evans, Professor W. J. Sollas, Dr. G- J. Hinde, and Messrs. 
W. CaiTuthers, R. B. Newton, J. J. H. Teall, F. W. Rudler, W. Topley, 
W. Whitaker, and E. Wethered be a Committee for the purpose of carry- 
ing on the Geological Record ; that Mr. W. Topley be the Secretary, and 
that the sum of 100?. be placed at their disposal for the purpose. 

That Mr. R. Etheridge, Dr. H. Woodward, and Professor T. R. Jones 
be reappointed a Committee for the purpose of reporting on the Fossil 
Phyllopoda of the Palseozoic Rocks ; that Professor T. R. Jones be the 
Secretary, and that the sum of 15?. be placed at their disposal for the 
purpose. 

Tbat Mr. Stainton, Sir John Lubbock,' and Mr. McLachlan be a 
Committee for the purpose of continuing a Record of Zoological Litera- 
ture ; that Mr. Stainton be the Secretary, and that the sum of 100?. be 
placed at their disposal for the purpose. 

That Mr. John Murray, Professor Cossar Ewart, Professor Alleyne 
Nicholson, Professor Mcintosh, Professor Young, Professor Struthers, 
and Professor McKendrick be reappointed a Committee for the purposes 
of a Marine Biological Station at Granton, Scotland ; that Mr. John 
Murray be the Secretary, and that the sum of 75?. be placed at their dis- 
posal for the purpose. 

That Professor Ray Lankester, Mr. P. L. Sclater, Professor M. Foster, 
Mr. A. Sedgwick, Professor A. M. Marshall, Professor A. C. Haddon, 
Professor Moseley, and Mr. Percy Sladen be reappointed a Committee for 
the purpose of arranging for the occasional occupation of a table at the 
Zoological Station at Naples ; that Mr. Percy Sladen be the Secretary, 
and that the sum of 50?. be placed at their disposal for the purpose. 

That Professor Cleland, Professor McKendrick, Professor Ewart, 
Professor Stirling, Professor Bower, Dr. Cleghorn, and Professor Mcintosh 
be a Committee for the purpose of continuing the Researches on Food 
Fishes and Invertebrates at the Marine Laboratory, St. Andrews ; that 
Professor Mcintosh be the Secretary, and that the sum of 75?. be placed 
at their disposal for the purpose. 

That Mr. J. Cordeaux, Mr. J. A. Harvie-Brown, Professor Newton, 
Mr. W. Eagle Clarke, Mr. R. M. Barrington, and Mr. A. G. More be 
appointed a Committee for the purpose of obtaining (with the consent 
of the Master and Elder Brethren of the Trinity House and the Commis- 
sioners of Northern and Irish Lights) observations on Migration at 
Lighthouses and Lightvessels, and of reporting on the same ; that Mr. 
J. Cordeaux be the Secretary, and that the sum of 30?. be placed at their 
disposal for the purpose. 

That Professor Cleland, Professor McKendrick, and Dr. McGregor- 
Robertson be a Committee for the purpose of investigating the 
Mechanism of the Secretion of Urine ; that Dr. McGregor- Robertson 
be the Secretary, and that the sum of 10?. be placed at their disposal 
for the purpose. 

That General J. T. Walker, Sir J. H. Lefroy, Lieut.- Colonel Godwin- 



Ixxiv REPORT — 1885. 

Austen, Mr. W. T. Blanford, Mr. Sclater, Mr. Carruthers, Mr. Thiselton- 
Dyer, Professor Strnthers, Mr. G. W. Bloxam, Mr. H. W. Bates, Lord 
Alfred Churcliill, Mr. F. Galton, Mr. J. S. O'Halloran, Mr. Coutts 
Trotter, and Professor Moseley be a Committee for the purpose of 
furthering the Exploration of New Guinea, by making a grant to Mr. 
Forbes for the purposes of his Expedition ; that Mr. H. W. Bates be the 
Secretary, and that the sum of 150/. be placed at their disposal for the 
purpose. 

That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson, 
Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Dr. Rae, 
Mr. H. W. Bates, and Captain W. J. Dawson be a Committee for the 
purpose of organising a systematic investigation of the Depth of the per- 
manently Frozen Soil in the Polar Regions, its geographical limits, and 
relation 'to the present Pole of greatest cold ; that Mr. H. W. Bates be the 
Secretary, and that the sum of 51. be placed at their disposal for the 
purpose. 

That Professor Sidgwick, Professor Foxwell, the Rev. W. Cunning- 
ham, and Professor Munro be a Committee for the purpose of inquiring 
into the Regulation of Wages under the Sliding Scales ; that Professor 
Munro be the Secretary, and that the sum of 10/. be placed at their dis- 
posal for the purpose. 

That Mr. W. H. Barlow, Professor J. Thomson, Captain D. Galton, 
Mr. B. Baker, Professor W. C. TJnwin, Professor A. B. W. Kennedy, Mr. 
C. Barlow, Mr. A. T. Atchison, and Professor H. S. Hele Shaw be a 
Committee for the purpose of obtaining information with reference ta 
the Endurance of Metals under repeated and varying stresses, and the 
proper working stresses on Railway Bridges and other structures subject 
to varying loads ; that Mi\ A. T. Atchison be the Secretary, and that 
the sum of 10/. be placed at their disposal for the purpose. 

That Dr. Garson, Mr. Pengelly, Mr. P. W. Rudler, and Mr. _G. W.. 
Bloxam be a Committee for the purpose of investigating the Prehistoric 
Race in the Greek Islands ; that Mr. Bloxam be the Secretary, and. 
that the sum of 20^. be placed at their disposal for the purpose. 

That Dr. E. B. Tylor, Dr. G. M. Dawson, General Sir J. H. Lefroy, Dr. 
Daniel Wilson, Mr. R. G. Haliburton, and Mr. George W. Bloxam be 
reappointed a Committee for the purpose of investigating and publishing 
reports on the physical characters, languages, and industrial and social 
condition of the North- Western Tribes of the Dominion of Canada ; that 
Mr. Bloxam be the Secretary, and that the sum of 50/. be placed at their 
disposal for the purpose. 

That Mr. Francis Galton, Dr. Beddoe, Mr. Brabrook, Professor 
Cunningham, Professor Flower, Mr. J. Park Harrison, Professor A. 
Macalister, Dr. Muirhead, Mr. F. W. Rudler, Professor Thane, and Dr. 
Garson be reappointed a Committee for the purpose of defining the 
Racial Characteristics of the Inhabitants of the British Isles ; that 
Dr. Garson be the Secretary, and that the sum of 10/. be placed at their 
disposal for the purpose. 

Not involving Grants of Money. 

That Mr. James N. Shoolbred and Sir William Thomson be reap- 
pointed a Committee for the purpose of reducing and tabulating the Tidal 
Observations in the English Channel made with the Dover tide-gauge, 



EECOMMENDATIOMS ADOPTED BT THE GENERAL COMMITTEE. IxxV 

and of connecting them with observations made on the French coast ; 
and that Mr. Shoolbred be the Secretary. 

That Professor Barrett, Professor Fitzgerald, and Professor Balfour 
Stewart be a Committee for the pnrpose of reporting on the Molecular 
Phenomena attending the Magnetisation of Iron ; and that Professor 
Barrett be the Secretary. 

That Professor G. H. Darwin and Professor J. C. Adams be reap- 
pointed a Committee for the Harmonic Analysis of Tidal Observations ; 
and that Professor Darwin be the Secretary. 

That Mr. John Murray, Professor Schuster, Sir William Thomson, 
Professor Sir H. B. Roscoe, Professor A. S. Herschel, Captain W. de W. 
Abney, Professor Bonney, Mr. R. H. Scott, and Dr. J. H. Gladstone be 
reappointed a Committee for the purpose of investigating the practica- 
bility of collecting and identifying Meteoric Dust, and of considering the 
question of undertaking regular observations in various localities ; and 
that Mr. Murray be the Secretary. 

That Professors A. Johnson, Macgregor, J. B. Cherriman, and H. J. 
Bovey and Mr. C. Carpmael be reappointed a Committee for the purpose 
of promoting Tidal Observations in Canada ; and that Professor Johnson 
be the Secretary. 

That Professor Sylvester, Professor Cayley, and Professor Salmon be 
reappointed a Committee for the purpose of calculating Tables of the 
Fundamental Invariants of Algebraic Forms ; and that Professor Cayley 
be the Secretary, 

That Professors Everett and Sir William Thomson, Mr. G. J. Symons, 
Sir A. C. Ramsay, Dr. A. Geikie, Mr. J. Glaisher, Mr. Pengelly, 
Professor Edward Hull, Professor Prestwich, Dr. C. Le Neve Foster, 
Professor A. S. Herschel, Professor G. A. Lebour, Mr. A. B. Wynne, 
Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wethered, 
and Mr. A. Strahan be reappointed a Committee for the purpose of 
investigating the Rate of Increase of Underground Temperature down- 
wards in various Localities of Dry Land and under Water ; and that Pro- 
fessor Everett be the Secretary. 

That Professor Cayley, Sir William Thomson, Mr. James Glaisher, 
and Mr, J. W. L. Glaisher (Secretary) be reappointed a Committee for 
the purpose of calculating certain tables in the Theory of Numbers 
connected with the divisors of a number. 

That Professors Tilden and Ramsay and Dr. W. W. J. Nicol be a 
Committee for the purpose of investigating the subject of Vapour Pressures 
and Refractive Indices of Salt Solutions ; and that Dr. W. W. J. Nicol 
be the Secretary. 

That Professors Ramsay, Tilden, Marshall, and W. L. Goodwin be 
a. Committee for the purpose of investigating certain Physical Constants 
of Solution, especially the expansion of saline solutions : and that Pro- 
fessor W. L. Goodwin be the Secretary. 

That Professors W. A. Tilden and H. E. Armstrong be a Committee 
for the purpose of investigating Isomeric Naphthalene Derivatives ; and 
that Professor H, E. Armstrong be the Secretary. 

That Professor Sir H. E. Roscoe, Mr. Lockyer, Professors Dewar, 
Liveing, Schuster, W. N. Hartley, and Wolcott Gibbs, Captain Abney, 
and Dr. Marshall Watts be a Committee for the purpose of preparing 
a new series of Wave-length Tables of the Spectra of the Elements ^ 
and that Dr. Marshall Watts be the Secretary. 



Ixxvi REPORT — 1885. 

That Professors Dewar and A. W. Williamson, Dr. Marshall Watts, 
Captain Abney, Dr. Johnstone Stoney, Professors W. N. Hartley, McLeod, 
Carey Foster, A. K. Huntington, Emerson Reynolds, Reinold, and 
Liveing, Lord Rayleigh, Professor Schuster, and Professor W. Chandler 
Roberts be a Committee for the purpose of reporting upon the present 
state of our knowledge of Spectrum Analysis ; and that Professor W. 
Chandler Roberts be the Secretary. 

That Professor E. Hull, Dr. H. W. Crosskey, Captain Douglas Galton, 
Professor J. Prestwich, and Messrs. James Glaisher, E. B. Marten, G. H. 
Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox 
Strangways, T. S. Stooke, G. J. Symons, W. Topley, Tylden- Wright, E. 
Wethered, W. Whitaker, and C. E. De Ranee be reappointed a Com- 
mittee for the purpose of investigating the Circulation of the Under- 
ground Waters in the Permeable Formations of England, and the Quality 
and Quantity of the Waters supplied to various towns and districts from 
these formations ; and that Mr. De Ranee be the Secretary. 

That Professors J. Prestwich, W. Boyd Dawkins, T. McK. Hughes, 
and T. G. Bonney, Dr. H. W. Crosskey, and Messrs. C. E. De Ranee, 
H. G. Fordham, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and 
R. H. Tiddeman be reappointed a Committee for the purpose of record- 
ing the position, height above the sea, lithological characters, size, and 
origin of the Erratic Blocks of England, Wales, and L-eland, reporting 
other matters of interest connected with the same, and taking measures 
for their preservation ; and that Dr. Crosskey be the Secretary. 

That Sir A. Taylor, Professor Bayley Balfour, Dr. Crombie Brown, 
Dr. Cleghorn, and Sir John Lubbock be a Committee for the purpose of 
considering whether the condition of our Forests and Woodlands might 
not be improved by the establishment of a Forest School. 

That Sir Joseph D. Hooker, Sir George Nares, Mr. John Murray, 
General J. T. Walker, Admiral Sir Leopold McClintock, Dr. W. B. 
Carpenter, Mr. Clements Markbam, and Admiral Sir Erasmus Ommanney, 
be a Committee for the purpose of drawing attention to the desirability 
of further research in the Antarctic Regions, nearly half a century having 
elapsed since the last exploration; and that Admiral Sir Erasmus 
■Ommanney be the Secretary. 

That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson, 
Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Mr. 
Francis Galton, Mr. H. W. Bates, and Mr. E. G. Ravenstein, with 
power to add to their number, be a Committee for the purpose of taking 
into consideration the combination of the Ordnance and Admiralty Sur- 
veys, and the production of a batho-hypsographical map of the British 
Islands ; and that Mr. E. G. Ravenstein be the Secretary. 

That General J. T. Walker, Sir William Thomson, Sir J. H. Lefroy, 
General R. Strachey, Professor A. S. Herschel, Professor G. Chrystal, 
Professor C. Niven, Professor J. H. Poynting, and Professor A. Schuster 
be a Committee for the purpose of inviting designs for a good Differential 
Gravity Meter in supersession of the pendulum, whereby satisfactory 
results may be obtained, at each station of observation, in a few hours, 
instead of the many days over which it is necessary to extend pendulum 
observations ; and that Professor J. H. Poynting be the Secretary. 

That Dr. J. H. Gladstone, Professor Armstrong, Mr. William Shaen, 
Mr. Stephen Bourne, Miss Lydia Becker, Sir John Lubbock, Dr. 
H. W. Crosskey, Sir Richard Temple, Sir Henry E. Roscoe, Mr. James 



EECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxvil 

Hey wood, and Professor N. Story Maskelyne be reappointed a Committee 
for the purpose of continuing the inquiries relating to the teaching of 
Science in Elementary Schools ; and that Dr. J. H. Gladstone be the 
Secretary. 

That the Corresponding Societies Committee, consisting of Mr. F. 
Galton, Professor "Williamson, Captain Douglas Galton, Professor Boyd 
Dawkins, Sir Rawson Rawson, Dr. Garson, Mr. J. Evans, Mr. J. 
Hopkinson, Mr. Whitaker, Mr. Symons, Professor Meldola (Secretary), 
and General Pitt- Rivers, be reappointed. 

That Mr. Mollison be requested to report on the present state of our 
knowledge of the Mathematical Theory of Thermal Conduction. 

That Mr. P. T. Main be requested to draw up a Report on our experi- 
mental knowledge of the Properties of Matter with respect to volume,, 
pressure, temperature, and specific heat. 

That Mr. Glazebrook be requested to continue his Report on Optics. 

That Professor J. J. Thomson be requested to continue his Report on. 
Electrical Theories. 

Communications ordered to be printed in extenso in the Annual 
Seport of the Association. 

Mr. Meldrum's paper, ' A Tabular Statement of the dates at which,, 
and the localities where Pumice or Volcanic Dust was seen in the 
Indian Ocean ' (with one plate). 

Professor 0. J. Lodge's paper ' On Electrolysis,' opening the discussion 
on Electrolysis. , 

Mr. Barker's paper ' On Slaty Cleavage.' 

That Mr. Whitaker be requested to enlarge his List of Works on the 
Geology of Staffordshire by the addition of lists on Warwickshire and 
Worcestershire, and that the same be printed in full in the Report. 

Mr. Stephen Bourne's paper ' On the use of Index Numbers in the 
Investigation of Trade Statistics.' 

Mr. W. H. Preece's paper ' On the Strength of Telegraph Poles.' 

Mr. A. S. Biggart's paper ' On the Forth Bridge Works,' with the 
necessary plates. 

Mr. J. N. Shoolbred's paper ' On the Electric Lighting of the Forth 
Bridge.' 

Mr. C. Barlow's paper ' On the Tay Bridge,' with the necessary plates^ 

Resolutions referred to the Council for Consideration, and Action if 

desirable. 

That the Council be requested to reconsider the proposal of holding a 
General International Congress, and to report to the General Committee 
thereon at the next Meeting of the Association. 

That the Council be requested to consider the desirability of admitting 
ladies as Officers of the Association, or as Members of the General or 
Sectional Committees. 

That the Council be requested to consider the advisability of renderino- 
the special Reports of the Association more accessible to the scientific 
public by placing them on sale in separate form. 

That the printed Reports on Special Subjects be oflPered for sale to- 



Ixxviii EEPOUT — 1885. 

the general public at the time of the Meeting, or as soon afterwards as 
possible. 

That the Conncil be requested to so modify the Rules of the Associa- 
tion as to permit of a Sectional Meeting being held at an earlier hour 
than eleven, and the Sectional Committee previously, due notice being 
given to the Section on the previous day. 

That a memorial be presented to H.M. Government requesting them 
to enlarge the existing Agricultural Department of the Privy Conncil, 
with the view of concentrating all administrative functions relating to 
Agriculture in one fully- equipped Board and Department of Agriculture. 

That the Council be requested to consider and take steps, if they think 
it desirable, to memorialise the Government to undertake the more 
systematic collection and annual publication of Statistics of Wages, and a 
periodical industrial census. 

That a memorial be presented to H.M. Government in favour of the 
establishment of a National School of Forestry. 



i 



SYNOPSIS jOF GEANTS OF MONEY. Ixxix 



Synopsis of Grants of Money appropriated to Scientific Pur- 
poses by the General Committee at the Aberdeen Meeting in 
September 1885. The Names of the Members entitled to 
call on the General Treasurer for the respective Grants are 
prefixed. 

Mathematics and Physics. 

£ s. d. 
*Foster, Professoi- G. Carey. — Electrical Standards 40 

*Stewart, Professor Balfour. — Solar Radiation 20 

*Stewart, Professor Balfour. — Meteorological Observations 

at Chepstow 25 

Darwin, Professor G. H. — Instructions for Tidal Observations 50 
*Stewart, Professor Balfour. — Comparing and reducing Mag- 
netic Observations 40 

*Forbes, Professor G. — Standards of Light , 20 

*Brown, Professor Crum. — Ben Nevis Observatory 100 

*Armstrong, Professor. — Physical and Chemical bearings of 

Electrolysis 20 



diemistry. 

M'Leod, Professor. — Silent discharge of Electricity into at- 
mosphere 20 

*Williamson, Professor A. W. — Chemical Nomenclature 6 



Geology. 

*Blanford, Mr. W. T.— Fossil plants of the Tertiary and 

Secondary Beds 20 

Hughes, Professor T. McK. — Caves of North Wales 25 

*Etheridge, Mr. R. — Volcanic Phenomena in Japan 50 

*Grantbam, R. B. — Erosion of Sea Coasts 20 

♦Bauerman, Mr. H. — Volcanic Phenomena of Vesuvius 30 

*E vans, Dr. J. — Geological Record 100 

^Etheridge, Mr. R. — Fossil Phyllopoda 15 



Carried forward ^600 

* Eeappointed. 



IXXX KEPOET 1885, 

& s. d. 
Brought forward 600 

Biology. 

*Stanton, Mr. H. T.— Zoological Record 100 

*Mrirray, Mr. J. — Marine Biological Station at Grantham ... 75 

*Lankester, Professor Ray. — Zoological Station at Naples ... 50 

Cleland, Professor. — Researches in Food Fishes and Inver- 

tebrata at St. Andrews 75 

*Cordeaux, Mr. J.— Migration of Birds 30 

Cleland, Professor. — Mechanism of Secretion of Urine 10 

Geography. 

Walker, General J. T. — New Guinea Exploration 150 0' 

Walker, General J. T. — Investigation into depth of perma- 
nently frozen soil in Polar Regions 5 0' 

Economic Science and Statistics. 

Sidgwick, Professor. — Regulation of Wages under sliding 

scales 10 

Mechanics. 
Barlow, Mr. W. H. — Effect of varying stresses on metals ... 10 

Anthropology. i 

Garson, Dr. — Investigation into a pre-historic race in the 

Greek Islands 20 

*Tylor, Dr. E. B. — Investigation into North- Western Tribes 

ofCanada 50 

*Galton, Mr. F. — Racial characteristics in British Isles 10 

£1195 
* Eeappointed. 



The Annual Meeting in 1886. 

The Meeting at Birmingham will commence on Wednesday, Sep- 
tember 1. 

Place of Meeting in 1887 . 

The Annual Meeting of the Association will be held at Manchester. 



GENERAL SXATEMEST. 



Ixxxi 



General Statement of Sums ivhich have been paid on account of 
Grants for Scientific Purposes. 



1834. 

Tide Discussions 20 

1835. 

Tide Discussions 62 

British Fossil Ichthyology ■■■ 105 

±'167 



1836. 

Tide Discussions 163 

British Fossillchthyology ... 105 
Thermometric Observations, 

&c 50 

Experiments on long-con- 
tinued Heat 17 1 

Eain-Gauges 9 13 

Refraction Experiments 15 

Lunar Nutation 60 

Thermometers 15 6 



£435 



1837. 

Tide Discussions 284 1 

Chemical Constants 24 13 6 

Lunar Nutation 70 

Observations on Waves 100 12 

Tides at Bristol 150 

Meteorology and Subterra- 
nean Temperature 93 3 

Vitrification Experiments ... 150 

Heart Experiments 8 4 6 

Barometric Observations 30 

Barometers 11 18 6 



£922 12 6 



1838. 

Tide Discussions 29 

British Fossil Fishes 100 

Meteorological Observations 
and Anemometer (construc- 
tion) 100 

Cast L-on (Strength of) 60 

Animal and Vegetable Sub- 
stances (Preservation of) ... 19 1 10 

Eailway Constants 41 12 10 

Bristol Tides 50 

Growth of Plants 75 

Mud in Rivers 3 6 6 

Education Committee 50 

Heart Experiments 5 3 

Land and Sea Level 267 8 7 

Steam-vessels 100 

Meteorological Committee ... 31 9 5 



£932 2 2 



1839. 

Fossillchthyology 110 

Meteorological Observations 

at Plymouth, &c 63 10 

1885. 



£ s. d. 

Mechanism of Waves 144 2 

Bristol Tides 35 18 6 

Meteorology and Subterra- 
nean Temperature 21 11 

Vitrification Experiments ... 9 4 7 

Cast-Iron Experiments 103 

Railway Constants 28 7 2 

Land and Sea Level 274 1 4 

Steam- vessels' Engines 100 

Stars in Histoire Celeste 171 18 6 

Stars in Lacaille 11 

Stars in R.A.S. Catalogue ... 166 16 6 

Animal Secretions 10 10 

Steam Engines in Cornwall... 50 

Atmospheric Air 16 1 

Cast and Wrought Iron 40 

Heat on Organic Bodies 3 

Gases on Solar Spectrum 22 

Hdurly Meteorological Ob- 
servations, Inverness and 

Kingussie 49 7 8 

Fossil Reptiles 118 2 9 

Mining Statistics 50 

£1595 11 

1840. 

Bristol Tides 100 a 

Subterranean Temperature ... 13 13 6 

Heart Experiments 18 19 

Lungs Experiments 8 13 

Tide Discussions 60 

Land and Sea Level 6 11 1 

Stars (Histoire Celeste) 242 10 

Stars (Lacaille) 4 15 

Stars (Catalogue) 264 0- 

Atmospheric Air 15 15 

Water on Iron 10 

Heat on Organic Bodies 7 & 

Meteorological Observations . 52 17 6 

Foreign Scientific Memoirs... 112 1 6 

Working Population 100 

School Statistics 50 

Forms of Vessels 184 7 

Chemical and Electrical Phe- 
nomena 40 

Meteorological Observations 

at Plymouth 80 

Magnetical Observations 185 13 9 



£1546 16 4 



1841. 

Observations on Waves 30 

Meteorology and Subterra- 
nean Temperature 8 

Actinometers 10 

Earthquake Shocks 17 

Acrid Poisons .. 6 

Veins and Absorbents 3 

Mud in Rivers 5 

e 







8 











7 
























Ixxxii 



KEPORT — 1885. 



£ s. d. 

Marine Zoology 15 12 8 

Skeleton Maps 20 

Mountain Barometers 6 18 6 

Stars (Histoire Celeste) 185 

Stars (Lacaille) 79 5 

Stars (Nomenclature of) 17 19 6 

Stars (Catalogue of ) 40 

Water on Iron 50 

Meteorological Observations 

at Inverness 20 

Meteorological Observations 

(reduction of ) 25 

Fossil Reptiles 50 

Foreign Memoirs 62 6 

Railvsray Sections 38 1 

Forms of Vessels 193 12 

Meteorological Observations 

at Plymouth 55 

Magnetical Observations 61 18 8 

Fishes of the Old Red Sand- 
stone 100 

Tides at Leith 50 

Anemometer at Edinburgh ... 69 1 10 

Tabulating Observations 9 6 3 

Races of Men 5 

Radiate Animals 2 

£1235 10 U 



18-12. 

Dynamometric Instruments . . 113 11 2 

Anoplura Britannice 52 12 

Tides at Bristol 59 8 

GasesonLight 30 14 7 

Chronometers 26 17 6 

Marine Zoology 15 

British Fossil Mammalia 100 

Statistics of Education 20 

Marine Steam-vessels' En- 
gines 28 

Stars (Tlistoire Celeste) ...... 69 

Stars (Brit. Assoc. Cat. of) ... 110 

Railway Sections 161 10 

British Belemnites .. 50 

Fossil Reptiles (publication 

of Report) 210 

Forms of Vessels 180 

Galvanic Experiments on 

Rocks 5 8 6 

Meteorological Experiments 

at Plymouth 68 

Constant Indicator and Dyna- 
mometric Instruments 90 

Force of Wind 10 

Light on Growth of Seeds ... 8 

Vital Statistics 50 

Vegetative Power of Seeds ... 8 1 11 

Questions on Human Race ... 7 9 

£1449 17 8 



1843. 
Revision of the Nomenclature 
of Stars 2 



£ s. d. 
Reduction of Stars, British 

Association Catalogue 25 

Anomalous Tides, Frith of 

Forth 120 

Hourly Meteorological Obser- 
vations at Kingussie and 

Inverness 77 12 8 

Meteorological Observations 

at Plymouth 55 

Whewell's Meteorological 

Anemometer at Plymouth . 10 
Meteorological Observations, 
Osier's Anemometer at Ply- 
mouth 20 

Reduction of Meteorological 

Observations 30 

Meteorological Instruments 

and Gratuities 39 6 

Construction of Anemometer 

at Inverness 56 12 2 

Magnetic Co-operation 10 8 10 

Meteorological Recorder for 

Kew Observatory 50 

Action of Gases on Light 18 16 1 

Establishment at Kew Ob- 
servatory, Wages, Repairs 
Furniture, and Sundries ... 133 4 7 
Experiments by Captive Bal- 
loons 81 8 

Oxidation of the Rails of 

Railways 20 

Publication of Report on 

Fossil Reptiles 40 

Coloured Drawings of Rail- 
way Sections 147 18 3 

Registration of Earthquake 

Shocks 30 

Report on Zoological Nomen- 
clature 10 

Uncovering Lower Red Sand- 
stone near Manchester 4 4 

Vegetative Power of Seeds ... 5 3 
Marine Testacea (Habits of) . 10 

Marine Zoology 10 

Marine Zoology 2 14 

Preparation of Report on Bri- 
tish Fossil Mammalia 100 

Physiological Operations of 

Medicinal Agents 20 

Vital Statistics 36 5 8 

Additional Experiments on 

the Forms of Vessels 70 

Additional Experiments on 

the forms of Vessels 100 

Reduction of Experiments on 

the Forms of Vessels 100 

Morin's Instrument and Con- 
stant Indicator 69 14 10 

Experiments on the Strength 
of Materials 



6 
8 


11 



... 60 








£1565 


10 


2 



GENERAL STATEMENT. 



Ixsxiii 



£ s. d. 
184i. 

Meteorological Observations 
at Kingussie and Inverness 12 

Completing Observations at 
PljTuouth 35 

Magnetic and Meteorological 

Co-operation 25 8 4 

Publication of the British 
Association Catalogue of 
Stars 35 

Observations on Tides on the 

East Coast of Scotland ... 100 

Revision of the Nomenclature 
of Stars 18i2 2 9 6 

Maintaining the Establish- 
ment in Kew Observa- 
tory 117 17 3 

Instruments for Kew Obser- 
vatory ... 56 7 3 

Influence of Light on Plants 10 

Subterraneous Temperature 

in Ireland 5 

Coloured Drawings of Rail- 
way Sections 15 17 6 

Investigation of Fossil Fishes 

of the Lower Tertiary Strata 100 

Registering the Shocks of 

Earthquakes 1842 23 11 10 

Structure of Fossil Shells ... 20 

Radiata and Mollusca of the 

^gean and Red Seas 1842 100 

Geographical Distributions of 

Marine Zoology 1842 10 

Marine Zoology of Devon and 

Cornwall 10 

Marine Zoology of Corfu 10 

Experiments on the Vitality 

of Seeds 9 

Experiments on the Vitality 
of Seeds 1842 8 7 3 

Exotic Anoplura 15 

Strength of Materials 100 

Completing Experiments on 

the Forms of Ships 100 

Inquiries into Asphyxia 10 

Investigations on the Internal 

Constitution of Metals 50 

Constant Indicator and Mo- 

rin's Instrument 1842 10 

■ £981 12 "8 

1845. 

Publication of the British As- 
sociation Catalogue of Stars 351 14 6 

Meteorological Observations 

at Inverness 30 IS 11 

Jlagnetic and Meteorological 

Co-operation 16 16 8 

Meteorological Instruments 

at Edinburgh 18 11 9 

Reduction of Anemometrical 

Observations at Plymouth 25 



£ s. d. 
Electrical Experiments at 

Kew Observatory 43 17 8 

Maintaining the Establish- 
ment in Kew Observatory 149 
For Kreil's Barometrograph 25 
Gases from Iron Furnaces... 50 

The Actinograph 15 

Microscopic Structure of 

Shells 20 

Exotic Anoplura 1843 10 

Vitality of Seeds 1843 2 

Vitality of Seeds 1844 7 

Marine Zoology of Cornwall 10 
Physiological Action of Medi- 
cines 20 

Statistics of Sickness and 

Mortality in York 20 

Earthquake Shocks 18 43 15 14 8 

£831 9~~9 



15 






































7 















1847. 
Computation of the Gaussian 

Constants for 1829 50 

Habits of Marine Animals ... 10 
Physiological Action of Medi- 
cines 20 

Blarine Zoology of Cornwall 10 

Atmospheric Waves 6 

Vitality of Seeds 4 

Maintaining the Establish- 
ment at Kew Observatory 107 

£208 



1846. 
British Association Catalogue 

of Stars 1844 211 15 

Fossil Fishes of the London 

Clay 100 

Computation of the Gaussian 

Constants for 1829 50 

Maintaining the Establish- 
ment at Kew Observatory 146 

Strength of Materials 60 

Researches in Asphyxia 6 

Examination of Fossil Shells 10 

Vitality of Seeds 1 844 2 

Vitality of Seeds 1845 7 

Marine Zoology of Cornwall 10 

Marine Zoology of Britain ... 10 

Exotic Anoplura 1814 25 

Expenses attending Anemo- 
meters 11 

Anemometers' Repairs 2 

Atmospheric Waves 3 

Captive Balloons 1844 8 

Varieties of the Human Race 

1844 7 6 3 
Statistics of Sickness and 

Mortality in York 12 

£685 16 



16 


7 








16 


2 








15 


10 


12 


3 




















7 


6 


3 


6 


3 


3 


19 


8 



























9 


3 


7 


7 



8 6 



5 4 



62 



Ixxxiv 



KEPORT — 1885. 



£ s. d. 
1848. 
Maintainingr the Establish- 
ment at Kew Observatory 171 15 11 

Atmospheric Waves 3 10 9 

Vitality of Seeds 9 15 

Completion of Catalogue of 

Stars 70 

On Colouring Matters 5 

On Growth of Plants •• 15 

£275 1 8 



1819. 

Electrical Observations at 

Kew Observatory 50 

Maintaining the Establish- 
ment at ditto 76 2 5 

Vitality of Seeds 5 8 1 

On Growth of Plants 5 

Kegistration of Periodical 

Phenomena 10 

Bill on Account of Anemo- 

metrical Observations 1 3 9 

£169 19 6 



1850. 
Maintaining the Establish- 
ment at Kew Observatory 255 18 
Transit of Earthquake "Waves 50 

Periodical Phenomena 15 

Meteorological Instruments, 

Azores 25 

£345 18 



1851 
Maintaining the Establish- 
ment at Kew Observatory 
(includes part of grant in 

1849) 309 2 2 

Theory of Heat 20 1 1 

Periodical Phenomena of Ani- 
mals and Plants 5 

Vitality of Seeds 5 6 4 

Influence of Solar Kadiation 30 

Ethnological Inquiries 12 

Researches on Annelida 10 

£391 9~7 



1852. 

Maintaining the Establish- 
ment at Kew Observatory 
(including balance of grant 
for 1850)... 233 17 8 

Experiments on the Conduc- 
tion of Heat 5 2 9 

Influence of Solar Radiations 20 

Geological Map of Ireland ... 15 

Researches on the British An- 
nelida 10 

Vitality of Seeds 10 6 2 

Strength of Boiler Plates 10 

£304 6 7 



£ ». d. 

1853. 

Maintaining the Establish- 
ment at Kew Observatory 165 

Experiments on the Influence 

of Solar Radiation 15 

Researches on the British 

Annelida 10 

Dredging on the East Coast 
of Scotland 10 

Ethnological Queries ^^ 5_ 



£205 a 



1854. 

Maintaining the Establish- 
ment at Kew Observatory 
(including balance of 
former grant) 330 15 4 

Investigations on Flax 11 

Effects of Temperature on 

Wrought Iron 10 

Registration of Periodical 

Phenomena 10 

British Annelida 10 

Vitality of Seeds 5 2 3 

Conduction of Heat 4 2 

£380 19 7 



18.55. 
Maintaining the Establish- 
ment at Kew Observatory 425 

Earthquake Movements 10 

Physical Aspect of the Moon 118 5 

Vitality of Seeds 10 7 11 

Map of the World 15 

Ethnological Queries 5 

Dredging near Belfast .^ 4 

£480T6~^ 



575 



1856. 
Maintaining the Establish- 
ment at Kew Observa- 
tory:— 

1854 £ 75 0\ 

1855 £500 0/ 

Strickland's Ornithological 

Synonyms 100 

Dredging and Dredging 

Forms 9 13 

Chemical Action of Light ... 20 Or 

Strength of Iron Plates 10 

Registration of Periodical 

Phenomena 10 

Propagation of Salmon 10 

£734 13 9- 



1857. 

Maintaining the Establish- 
ment at Kew Observatory 350 

Earthquake Wave Experi- 
ments 40 

Dredging near Belfast 10 O' 

Dredging on the West Coast 
of Scotland 10 a 



GENERAL STATEMENT. 



Ixxxv 



5 7 


4 


... 5 





£507 15 


4 



£ s. d. 

Investigations into the Mol- 

lusca of California 10 

Experiments on Flax 5 

Natural History of Mada- 
gascar 20 

Researches on British Anne- 
lida 25 

Eeport on Natural Products 

imported into Liverpool ... 10 

Artificial Propagation of Sal- 
mon 10 

Temperature of Mines 7 8 

Thermometers for Subterra- 
nean Observations 

Life-boats 

18.58. 

Maintaining the Establish- 
ment at Kew Observatory 500 

Earthquake Wave Experi- 
ments 25 

Dredging on the West Coast 
of Scotland 10 

Dredging near Dublin 5 

Vitality of Seeds 5 5 

Dredging near Belfast 18 13 2 

Report on the British Anne- 
lida 25 

Experiments on the produc- 
tion of Heat by Motion in 
Fluids 20 

Report on the Natural Pro- 
ducts imported into Scot- 
land 10 

£618 18 2 

1859. 
Maintaining the Establish- 
ment at Kew Observatory 500 

Dredging near Dublin 15 

Osteology of Birds 50 

Irish Tunicata 5 

Manure Experiments 20 

British Medusidas 5 

Dredging Committee 5 

Steam-vessels' Performance... 5 
Marine Fauna of South and 

AVest of Ireland 10 

Photographic Chemistry 10 

Lanarljshire Fossils 20 1 

Balloon Ascents 39 11 

£684 11 1 

1860. 

Maintaining the Establish- 
ment at Kew Observatory 500 

Dredging near Belfast 16 6 

Dredging in Dublin Bay 15 

Inquiry into the Performance 

of Steam-vessels ]24 

Explorations in the Yellow 
Sandstone of Dura Don ... 20 



Chemico-mechanical Analysis 

of Rocks and Minerals 25 

Researches on the Growth of 

Plants 10 

Researches on the Solubility 

of Salts 30 

Researches on the Constituents 

of Manures 25 

Balance of Captive Balloon 

Accounts 1 



». d, 









13 6 



£766 19 6 



1861. 
Maintaining the Establish- 
ment of Kew Observatory.. 500 

Earthquake Experiments 25 

Dredging North and East 

Coasts of Scotland 23 

Dredging Committee : — 

1860 £50 \ 

1861 £22 0/ 

Excavations at Dura Den 20 

Solubility of Salts 20 

Steam- vessel Performance ... 150 

Fossils of Lesmahago 15 

Explorations at Uriconium... 20 

Chemical Alloys 20 

Classified Index to the Trans- 
actions 100 

Dredging in the Mersey and 

Dee 5 

Dip Circle 30 

Photoheliographic Observa- 
tions 50 

Prison Diet 20 

Gauging of Water 10 

Alpine Ascents 6 

Constituents of Manures 25 










72 











































































5 


10 









£1111 5 10 



1862. 
Maintaining the Establish- 
ment of Kew Observatory 500 

Patent Laws 21 

Mollusca of N.- W. of America 10 
Natural History by Mercantile 

Marine 5 

Tidal Observations 25 

Photoheliometer at Kew 40 

Photographic Pictures of the 

Sun 150 

Rocks of Donegal 25 

Dredging Durham and North- 
umberland 25 

Connexion of Storms 20 

Dredging North-east Coast 

of Scotland 6 

Ravages of Teredo 3 

Standards of Electrical Re- 
sistance 50 

Railway Accidents 10 

Balloon Committee 200 

Dredging Dublin Bay 10 









6 





















































9 


6 


11 






























Jxxxvi 



repout — 1885. 



£ s. d. 

Dredging the Mersey 5 

Prison Diet 20 

Gauging of Water 12 10 

Steamships' Performance 150 

Thermo- Electric Currents 5 

£1293 16 6 



18C3. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 
Balloon Committee deficiency 70 
Balloon Ascents (other ex- 
penses) 25 

Entozoa 25 

Coal Fossils 20 

Herrings 20 

Granites of Donegal 5 

Prison Diet 20 

Vertical Atmospheric Move- 
ments 13 

Dredging Shetland 50 

Dredging North-east coast of 

Scotland 25 

Dredging Northumberland 

and Durham 17 

Dredging Committee superin- 
tendence 10 

Steamship Performance 100 

Balloon Committee 200 

Carbon under pressure 10 

Volcanic Temperature 100 

Bromide of Ammonium 8 

Electrical Standards 100 

Electrical Construction and- 

Distribution 40 

Luminous Meteors 17 

Kew Additional Buildings for 

Photoheliograph 100 

Thermo-EIectricity 15 

Analysis of Eocks 8 

Hydroida 10 

£1608 




































































3 10 


















































































3 10 



1864. 
Maintaining tlie Establish- 
ment of Kew Observatory.. 600 

Coal Fossils 20 

Vertical Atmospheric Move- 
ments 20 

Dredging Shetland 75 

Dredging Northumberland... 25 

Balloon Committee 200 

Carbon under pressure 10 

Standards of Electric Ke- 

sistance 100 

Analysis of Piocks 10 

Hydroida 10 

Askham's Gift 50 

Nitrite of Amyle 10 

Nomenclature Committee ... 5 

Eain-Gauges 19 15 8 

Cast-iron Investigation 20 



£ s. d 
Tidal Observations in the 

Humber 50 

Spectral Kays 45 

Luminous Meteors 20 

£1289 15 8 
1865. — — — — 
Maintaining the Establish- 
ment of kew Observatory.. 600 

Balloon Committee 100 

Hydroida 13 

Eain-Gauges 30 

Tidal Observations in the 

Humber 6 8 

Hexylic Compoimds 20 

Amyl Compounds 20 

Irish Flora 25 

American Mollusca 3 9 

Organic Acids 20 

Lingula Flags Excavation ... 10 

Eurj^Dterus 50 

Electrical Standards 100 

Malta Caves Eesearches 30 

Oyster Breeding 25 

Gibraltar Caves Eesearches... 150 

Kent's Hole Excavations 100 

Moon's Surface Observations 35 

Marine Fauna 25 

Dredging Aberdeenshire 25 

Dredging Channel Islands ... 50 

Zoological Nomenclature 5 

Eesistance of Floating Bodies 

inAVater 100 

Bath Waters Analysis 8 10 10 

Luminous Meteors 40 

£1591 7 10 

1866. 
Maintaining the Establish- 
ment of Kew Observatory. . 600 

Lunar Committee 64 13 4 

Balloon Committee 50 

Metrical Committee 60 

British Eainfall 50 

Kilkenny Coal Fields 16 

Alum Bay Fossil Leaf-Bed ... 15 

Luminous Meteors 50 

Lingula Flags Excavation ... 20 
Chemical Constitution of 

Cast Iron 60 

Amyl Compotinds 25 

Electrical Standards 100 

Malta Caves Exijloration 30 

Kent's Hole Exploration 200 

Marine Fauna, &c., Devon 

and Cornwall 25 

Dredging Aberdeenshire Coast 25 

Dredging Hebrides Coast ... 60 

Dredging the Mersey 5 

Eesistance of Floating Bodies 

in Water 60 

Polycyanidesof Organic Eadi- 

cals 29 



GENERAL STATEMENT. 



Ixxxvii 



£ s. d. 

Riffor Mortis 10 

Irish Annelida 15 

Catalogue of Crania 50 

Didine Birds of Mascarene 

Islands 50 

Tj'pical Crania Researches ... 30 

Palestine Exploration Fun d... 100 

:gl750 13 4 

1867. 
Maintaining the Establish- 
ment of Kew Observatory.. 600 
Meteorological Instruments, 

Palestine..... 50 

Lunar Committee 120 

Metrical Committee 30 

Kent's Hole Explorations ... 100 

Palestine Explorations 50 

Insect Fauna, Palestine 30 

British Rainfall 50 

Kilkenny Coal Fields 25 

Alum Bay Fossil Leaf -Bed ... 25 

Luminous Meteors 50 

Bournemouth, &c., Leaf-Beds 30 

Dredging Shetland 75 

Steamship Reports Condensa- 
tion 100 

Electrical Standards 100 

Ethyl and Methyl series 25 

Fossil Crustacea 25 

Sound under Water 24 4 

North Greenland Fauna 75 

Do. Plant Beds 100 

Iron and Steel Manufacture... 25 

Patent Laws 30 

£1739 4 

1868. 
Maintaining the Establish- 
ment of Kew Observatory. . 600 

Lunar Committee 120 

Metrical Committee 50 

Zoological Record 100 

Kent's Hole Explorations ... 150 

Steamship Performances 100 

British Rainfall 50 

Luminous Meteors 50 

Organic Acids 60 

Fossil Crustacea 25 

Methyl Series 25 

Mercury and Bile 25 

Organic Remains in Lime- 
stone Rocks 25 

Scottish Earthquakes 20 

Fauna, Devon and Cornwall.. 30 

British Fossil Corals 50 

Bagshot Leaf-Beds 50 

Greenland Explorations 100 

Fossil Flora : 25 

Tidal Observations 100 

Underground Temperature ... 50 
Spectroscopic Investigations 

of Animal Substances 5 



Secondary Reptiles, &c 30 

British Marine Invertebrate 

Fauna -. 100 

£1'J40 

1869. *^^^ 
Maintaining the Establish- 
ment of Kew Observatory. . 600 

Lunar Committee 50 

Metrical Committee 25 

Zoological Record 100 

Committee on Gases in Deep- 
well Water 25 

British Rainfall 50 

Thermal Conductivity of Iron, 

&c 30 

Kent's Hole Explorations 150 

Steamship Performances 30 

Chemical Constitution of 

Cast Iron 80 

Iron and Steel Manufacture 100 

Methyl Series 30 

Organic Remains in Lime- 
stone Rocks 10 

Earthquakes in Scotland 10 

British Fossil Corals 50 

Bagshot Leaf-Beds 30 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature ... 30 
Spectroscopic Investigations 

of Animal Substances 5 

Organic Acids 12 

Kiltorcan Fossils 20 

Chemical Constitution and 
Physiological Action Rela- 
tions 15 

Mountain Limestone Fossils 25 

Utilization of Sewage 10 

Products of Digestion 10 

£1622' 

1870. 
Maintaining the Establish- 
ment of Kew Observatory 600 

Metrical Committee 25 

Zoological Record 100 

Committee on Marine Fauna 20 

Ears in Fishes 10 

Chemical Nature of Cast Iron 80 

Luminous Meteors 30 

Heat in the Blood 15 

British Rainfall 100 

Thermal Conductivity of 

Iron, &c : 20 

British Fossil Corals 50 

Kent's Hole Explorations ... 150 

Scottish Earthquakes 4 

Bagshot Leaf- Beds 15 

Fossil Flora 25 

Tidal Observations 100 

Underground Temperature ... 50 

Kiltorcan Quarries Fossils ... 20 



«. d. 























































































































































































































































































Ixxxviii 



EEPORT — 1885. 



£ 
Mountain Limestone Fossils 25 

Utilization of Sewage 50 

Organic Chemical Compounds 30 

Onny River Sediment 3 

Mechanical Equivalent of 

Heat ••• 50 

£1572 

J871. 
Maintaining the Establish- 
ment of Kew Observatory 600 
Monthly Reports of Progi'ess 

in Chemistry 100 

Metrical Committee 25 

Zoological Record 100 

Thermal Equivalents of the 

Oxides of Chlorine 10 

Tidal Observations 100 

Fossil Flora 25 

Luminoiis Meteors 30 

British Fossil Corals 25 

Heat in the Blood 7 

British Rainfall 50 

Kent's Hole Explorations ... 150 

Fossil Crustacea 25 

Methyl Compounds 25 

Lunar Objects 20 

Fossil Coral Sections, for 

Photographing 20 

Bagshot Leaf-Beds 20 

Moab Explorations 100 

Gaussian Constants 40 

£1472 

1872. 
Maintaining the Establish- 
ment of Kew Observatory 300 

Metrical Committee 75 

Zoological Record 100 

Tidal Committee 200 

Carboniferous Corals 25 

Organic Chemical Compounds 25 

Exploration of Moab 100 

Terato-Embryological Inqui- 
ries 10 

Kent's Cavern Exploration.. 100 

Luminous Meteors 20 

Heat in the Blood 15 

Fossil Crustacea 25 

Fossil Elephants of Malta ... 25 

Lunar Objects 20 

Inverse Wave-Lengths 20 

British Rainfall 100 

Poisonous Substances Antago- 
nism 10 

Essential Oils, Chemical Con- 
stitution, &c 40 

Mathematical Tables 50 

Thermal Conductivity of Me- 
tals 



s. d. 





































































2 


6 

























































2 6 






















































































































.... 25 












£1285 









£ s. d. 
1873. 

Zoological Record 100 

Chemistry Record 200 

Tidal Committee 400 

Sewage Committee 100 

Kent's Cavern Exploration ... 150 

Carboniferous Corals 25 

Fossil Elephants 25 

Wave-Lengths 150 

British Rainfall 100 

Essential Oils 30 

Mathematical Tables 100 

Gaussian Constants •.... 10 

Sub-Wealden Explorations... 25 

Underground Temperature ... 150 

Settle Cave Exploration 50 

Fossil Flora, Ireland 20 

Timber Denudation and Rain- 
fall 20 

Luminous Meteors .'^O 

£1685 

1874. "* ■ 

Zoological Record 100 

Chemistry Record 100 

Mathematical Tables 100 

Elliptic Functions 100 

Lightning Conductors 10 

Thermal Conductivity of 

Rocks 10 

Anthropological Instructions, 

&c 50 

Kent's Cavern Exploration... 150 

Luminous Meteors 30 

Intestinal Secretions 15 

British Rainfall 100 

Essential Oils 10 

Sub-Wealden Explorations... 25 

Settle Cave Exploration 50 

Mauritius Meteorological Re- 
search 100 

Magnetization of Iron 20 

Marine Organisms 30 

Fossils, North- West of Scot- 
land 2 10 

Physiological Action of Light 20 

Trades Unions 25 

Mountain Limestone-Corals 25 

Erratic Blocks 10 

Dredging, Durham and York- 
shire Coasts 28 5 

High Temperature of Bodies 30 

Siemens 's Pyrometer 3 6 

Labyrinthodonts of Coal- 

Measures 7 15 

£1151 16 

1875. 

Elliptic Functions 100 

Magnetization of Iron 20 

British Rainfall 120 

Luminous Meteors 30 

Chemistry Record 100 



GENERAL STATEMENT. 



Ixxxix 



£ s. d. 

Specific Volume of Liquids... 25 
Estimation of Potash and 

Phosphoric Acid 10 

Isometric Cresols 20 

Sub- Wealden Explorations... 100 

Kent's Cavern Exploration... 100 

Settle Cave Exploration 50 

Earthquakes in Scotland 15 

Underground Waters 10 

Development of Myxinoid 

Fishes 20 

Zoological Record 100 

Instructions for Travellers ... 20 

Intestinal Secretions 20 

Palestine Exploration 100 

£960 



1876. 

Printing Mathematical Tables 159 4 2 

British Rainfall 100 

Ohm's Law 9 15 

Tide Calculating Machine ... 200 

Specific Volume of Liquids... 25 

Isomeric Cresols 10 

Action of Ethyl Bromobuty- 

rate on Ethyl Sodaceto- 

acetate 5 

Estimation of Potash and 

Phosphoric Acid 13 

Exploration of Victoria Cave, 

Settle 100 

Geological Record 100 

Kent's Cavern Exploration... 100 
Thermal Conductivities of 

Rocks 10 

Underground Waters 10 

Earthquakes in Scotland 1 10 

Zoological Record 100 

Close Time 5 

Physiological Action of Sound 25 

Zoological Station 75 

Intestinal Secretions 15 

Physical Characters of Inha- 
bitants of British Isles 13 15 

Measuring Speed of Ships ... 10 
Effect of Propeller on turning 

of Steam Vessels 5 

£1092 4 2 



1877. 
Liquid Carbonic Acids in 

Minerals 20 

Elliptic Functions 250 

Thermal Conductivity of 

Rocks 9 11 7 

Zoological Record 100 

Kent's Cavern 100 

Zoological Station at Naples 75 

Luminous Aleteors 30 

Elasticity of Wires 100 

Dipterocarpse, Report on 20 



£ «. d. 
Mechanical Equivalent of 

Heat 35 

Double Compounds of Cobalt 

and Nickel 8 

Underground Temperatures 50 

Settle Cave Exploration 100 

Underground Waters in New 

Red Sandstone 10 

Action of Ethyl Bromobuty- 

rate on Ethyl Sodaceto- 

acetate 10 

British Earthworks 25 

Atmospheric Elasticity in 

India 15 

Development of Light from 

Coal-gas 20 

Estimation of Potash and 

Phosphoric Acid 1 18 

Geological Record 100 

Anthropometric Committee 34 
Physiological Action of Phos- 
phoric Acid, &c 15 

£1128 9 7 



1878. 
Exploration of Settle Caves 100 

Geological Record 100 

Investigation of Pulse Pheno- 
mena by means of Syphon 

Recorder 10 

Zoological Station at Naples 75 
Investigation of Underground 

Waters 15 

Transmission of Electrical 

Impulses through Nerve 

Structure 30 

Calculation of Factor Table 

of Fourth Million 100 

Anthropometric Committee... 66 
Chemical Composition and 

Structure of less known 

Alkaloids 25 

Exploration of Kent's Cavern 50 

Zoological Record 100 

Fermanagh Caves Exploration 15 
Thermal Conductivity of 

Rocks 4 16 6 

Luminous Meteors 10 

Ancient Earthworks 25 

£725 16 6 

1879. 

Table at the Zoological 

Station, Naples 75 

Miocene Flora of the Basalt 

of the North of Ireland ... 20 

Illustrations for a Monograph 

on the Mammoth 17 

Record of Zoological Litera- 
ture 100 

Composition and Structure of 
less-known Alkaloids ^ - 25 



xc 



REPORT — 1 885. 



£ s. d. 

Exploration of Caves in 

Borneo 50 

Kent's Cavern Exploration... 100 

Kecord of the Progress of 

Geology 100 

Fermanagh Caves Exploration 5 

Electrolysis of Metallic Solu- 
tions and Solutions of 
Compound Salts 25 

Anthropometric Committee... 50 

Natural History of Socotra... 100 

Calculation of Factor Tables 

for 5th and 6th Millions ... 150 

Circulation of Underground 
Waters 10 

Steering of Screw Steamers... 10 

Improvements in Astrono- 
mical Clocks 30 

Marine Zoology of South 

Devon 20 

Determination of Mechanical 

Equivalent of Heat 12 15 6 

Specific Inductive Capacity 

of Sprengel Vacuum 40 

Tables of Sun-heat Co- 
efficients 30 

Datum Level of the Ordnance 

Survey 10 

Tables of Fundamental In- 
variants of Algebraic Forms 36 14 9 

AtmosiDheric Electricity Ob- 
servations in Madeira 15 

Instrument for Detecting 

Fire-damp in Mines 22 

Instruments for Measuring 

the Speed of Ships 17 1 8 

Tidal Observations in the 

English Channel 10 

£1 080 11 11 

1880. 

New Form of High Insulation 

Key 10 

Underground Temperature ... 10 

Determination of the Me- 
chanical Equivalent of 
Heat 8 6 

Elasticity of Wires 50 

Luminous Meteors 30 

Lunar Disturbance of Gravity 30 

Fundamental Invariants 8 5 

Laws of Water Friction 20 

Sj)ecific Inductive Capacity 

of Sprengel Vacuum 20 

Comp)letion of Tables of Sun- 
heat Coefficients 50 

Instrument for Detection of 

Fire-damp in Mines 10 

Inductive Capacity of Crystals 

and Paraffines 4 17 7 

Report on Carboniferous 

Polyzoa 10 



£ s. d. 

Caves of South Ireland 10 

Viviparous Nature of Ichthyo- 
saurus 10 

Kent's Cavern Exploration... 60 

Geological Record 100 

l\Iiocene Flora of the Basalt 

of North Ireland 15 

Underground Waters of Per- 
mian Formations 5 

Record of Zoological Litera- 
ture 100 

Table at Zoological Station 

at Naples 76 

Investigation of the Geology 

and Zoology of Mexico 50 

Anthropometry 50 

Patent Laws 5 

£731 7 7 



1881. 

Lunar Disturbance of Gravity 30 

Underground Temperature ... 20 

High Insulation Key 5 

Tidal Observations 10 

Fossil Polyzoa 10 

Underground Waters 10 

Earthquakes in Japan 25 

Tertiary Flora 20 

Scottish Zoological Station ... 50 

Naples Zoological Station ... 75 

Natural History of Socotra ... 50 

Zoological Record 100 

Weights and Heights of 

Human Beings 30 

Electrical Standards 25 

Anthropological Notes and 

Queries 9 

Specific Refractions 7 

£476 

1882. 
Tertiarj' Flora of North of 

Ireland 20 

Exploration of Caves of South 

of Ireland 10 

Fossil Plants of Halifax 15 

Fundamental Invariants of 

Algebraical Forms 76 

Record of Zoological Litera- 
ture 100 

British Polyzoa 10 

Naples Zoological Station ... 80 

Natural History of Timor- laut 100 
Conversion of Sedimentary 
Materials into Metamorphic 

Rocks 10 

Natural History of Socotra... 100 
Circulation of Underground 

Waters 15 

Migration of Birds 15 

Earthquake Phenomena of 

Japan 25 

























































































3 1 



3 1 









1 11 























GENERAL STATEMENT. 



XCl 



& 
Geological Map of Europe ... 25 
Elimination of Nitrogen by 

Bodily Exercise 50 

Anthropometric Committee... 50 
Photograpliing Ultra- Violet 

Spark Spectra 25 

Exploration of Kaygill Fis- 
sure 20 

Calibration of Mercurial Ther- 
mometers 20 

Wave-length Tables of Spec- 
tra of Elements 50 

Geological Eecord 100 

Standards for Electrical 

Measurements 100 

Exploration of Central Africa 100 
Albuminoid Substances of 
Serum 10 

£1126 

1883. 
Natural History of Timor-laut 50 

British Fossil iPolyzoa 10 

Circulation of Underground 

Waters 15 

Zoological Literature Eecord 100 
Exploration of Mount Kili- 

ma-njaro 500 

Erosion of Sea-coast of Eng- 
land and Wales 10 

Fossil Plants of Halifax 20 

Elimination of Nitrogen by 

Bodily Exercise 38 

Isomeric Naphthalene Deri- 
vatives 15 

Zoological Station at Naples 80 
Investigation of Loughton 

Camp 10 

Earthquake Phenomena of 

Japan 50 

Meteorological Observations 

on Ben Nevis 50 

Fossil Phyllopoda of Palaeo- 
zoic Eocks 25 

Migration of Birds 20 

Geological Eecord 50 

Exploration of Caves in South 

of Ireland 10 

Scottish Zoological Station... 25 
Screw Gauges 5 

£1083~ 

1884. 

Zoological Literature Eecord 100 

Fossil Polyzoa 10 

Exploration of Mount Kili- 

ma-njaro, East Africa 500 

Anthropometric Committee... 10 

Fossil Plants of Halifax 15 

International Geological Map 20 

Erratic Blocks of England ... 10 

Natural History of Timor-laut 50 



s. d. 

























1 11 













































3 


3 




































































3 


3 



















































£ s. d. 

Coagulation of Blood 100 

Naples Zoological Station ... 80 
Bibliography of Groups of 

Invertebrata 50 

Earthquake Phenomena of 

Japan 75 

Fossil Phyllopoda of Paleo- 
zoic Eocks 15 

Meteorological Observatory at 

Chepstow 25 

Migration of Birds 20 

Collecting and Investigating 

Meteoric Dust 20 

Circulation of Underground 

Waters 5 

Ultra- Violet Spark Spectra ... 8 4 

Tidal Observations 10 

Meteorological Observations 

on Ben Nevis 50 

£1173 4 



1885. 

Zoological Literature Eecord. 100 

Vapour Pressures, &c., of Salt 

Solutions 25 

Physical Constants of Solu- 
tions 20 

Eecent Polyzoa 10 

Naples Zoological Station ... 100 

Exploration of Mount Kilima- 
njaro 25 

Fossil Plants of British Ter- 
tiary and Secondary Beds . 50 

Calculating Tables in Theory 
of Numbers 100 

Exploration of New Guinea... 200 

Exploration of Mount Eo- 

raima 100 

Meteorological Observations 
on Ben Nevis 50 

Volcanic Phenomena of Vesu- 
vius 25 

Biological Stations on Coasts 
of United Kingdom 150 

Meteoric Dust 70 

Marine Biological Station at 
Granton loo 

Fossil Phyllopoda of Palajozoic 

Eocks 25 

Migration of Birds 30 

Synoptic Chart of Indian 
Ocean 50 

Circulation of Underground 
Waters 10 

Geological Eecord 50 

Eeduction of Tidal Observa- 
tions 10 

Earthquake Phenomena of 
Japan 70 

Eaygill Fissure 15 

£1385 6 



XCii BEPOET — 1885. 

General Meetings. 

On Wednesday, September 9, at 8 p.m., in tlie Music Hall, the Right 
Hon. Lord Rayleigh, M.A., D.C.L., LL.D., F.R.S., F.R.A.S., F.R.G.S., 
resigned the office of President to the Right Hon. Sir Lyon Playfair, 
K.C.B., M.P., Ph.D., LL.D., F.R.S. L. & B., F.C.S., who took the Chair, 
and delivered an Address, for which see page 1. 

On Thursday, September 10, at 8 p.m., a Soiree took place in the Art 
Gallery. 

On Friday, September 11, at 8 p.m., in the Music Hall, Professor 
W. G. Adams, M.A., F.R.S., F.G.S., delivered a Discourse on ' The 
Electric Light and Atmospheric Absorption.' 

On Monday, September 14, at 8.30 p.m., in the Music Hall, Mr. John 
Murray, F.R.S.E., delivered a Discourse on ' The Great Ocean Basins.' 

On Tuesday, September 15, at 8 p.m., a Soiree took place in the Art 
Gallery. 

On Wednesday, September 16, at 2.30 p.m., the concluding General 
Meeting took place in St. Katherine's Hall, when the Proceedings of the 
General Committee and the Grants of Money for Scientific purposes 
were explained to the Members. 

The Meeting was then adjourned to Birmingham. [The Meeting is 
appointed to commence on Wednesday, September 1, 1886.] 



PEE SIDE NT'S ADDEESS. 



1885. 



ADDEESS 



BY 



THE EIGHT HOX. SHI LYON PLAYFAIE, 

K.C.B., M.P., F.R.S. 
PRESIDENT. 



I. Visit to Canada. 

OuE meeting at Montreal was a notable event in the life of the Brit- 
ish Association, and even marked a distinct epoch in the histoiy of 
civilisation. It was by no mere accident that the constitntion of the 
Association enabled it to embrace all parts of the British Empire. Science 
is truly catholic, and is bounded only by the universe. lu relation to 
our vast empire, science, as well as literature and art, is the common 
possession of all its varying people. The United Kingdom is limited to 
120,800 square miles, inhabited by 35 millions of people ; but the empire 
as a whole has 8^ millions of square miles, with a population of 305 millions. 
To federate such vast possessions and so teeming a population into a political 
unit is a work only to be accomplished by the labours and persistent 
efforts of perhaps several generations of statesmen. The federation of its 
science is a subject of less dimensions well within the range of experi- 
ment. No part of the British Empire was more suited than Canada to 
try whether her science could be federated with our science. Canada 
has lately federated distinct provinces, with conflicting interests arising 
from difference of races, nationalities, and religions. PoHtical federation 
is not new in the history of the world, though it generally arises as a 
consequence of war. It was war that taught the Netherlands to federate 
in 1619. It was war which united the States in America ; federated 
Switzerland, Germany, and Austria, and unified Italy. But Canada 
formed a great national life out of petty provincial existences in a time 
of profound peace. This evolution gave an immense impulse to her 
national resources. The Dominion still requires consolidation in its vast 
extent, and applied science is rapidly effecting it. Canada, with its great 
expanse of territory, nearly as large as the United States, is being knit 

b2 



4 REroTiT — 1885. 

together by the iron bands of railways from the Gulf of St. Lawrence to 
the Pacific Ocean, so that the fertile lands of Ontario, Manitoba, Columbia, 
and the North-TVestern Territories will soon be available to the world. 
Still practical science has much to accomplish. England and France, 
with only one-fifth the fertile area of Canada, support 80 millions of 
people, while Canada has a population not exceeding 5 millions. 

A less far-seeing people than the Canadians might have invited the 
applied science which they so much require. But they knew that with- 
out science there are no applications. They no doubt felt with Emerson — 

And what if Trade sow cities 
Like shells along the shore, 
And thatch with towns the prairie broad 
With railwaj's ironed o'er ; 
The}' are but sailing foam-bells 
Along Thought's causing stream. 
And take their shape and sun-colour 
From liim that sends the dream. 

So it was with a far-reaching foresight that the Canadian Government 
invited the British Association for the Advancement of Science to meet 
in Montreal. The inhabitants of Canada received us with open arms, 
and the science of the Dominion and that of the United Kingdom were 
welded. We found in Canada, as we had every reason to expect, men of 
manly and self-reliant character who loved not less than we did the old 
home from which they had come. Among them is the same healthi- 
ness of political and moral life, with the same love of truth which dis- 
tinguishes the English people. Our great men are their great men ; our 
Shakspcare, Milton, and Burns belong to them as much as to ourselves ; 
our Newton, Dalton, Faraday, and Darwin are their men of science as 
much as they are ours. Thus a common possession and mutual sympathy 
made the meeting in Canada a successful effort to stimulate the progress 
of science, while it established, at the same time, the principle that all 
people of British origin — and I would fain include our cousins in the 
United States — possess a common interest in the intellectual glories of 
their race, and ought, in science at least, to constitute part and parcel of 
a common empire, whose heart may beat in the small islands of the 
Northern seas, but whose blood circulates in all her limbs, carrying 
warmth to them and bringing back vigour to us. Nothing can be more 
cheering to our Association than to know that many of the young com- 
munities of English-speaking people all over the globe — in India, China, 
Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have 
founded scientific societies in order to promote the growth of scientific 
research. No doubt science, which is only a form of truth, is one in all 
lands, but still its unity of purpose and fulfilment received an important 
practical expression by our visit to Canada. This community of science 
will be continued by the fact that we have invited Sir William Dawson, . 
of Montreal, to be our next President at Birmingham, 



ADDRESS. O 

II. Science and the State. 

I cannot address you in Aberdeen without recollecting that when we 
last met in this city our President was a great prince. The just verdict 
of time is that, high as was his royal rank, he has a far nobler claim to 
our regard as a lover of humanity in its widest sense, and especially as a 
lover of those arts and sciences which do so much to adorn it. On 
September 14, 1859, I sat on this platform and listened to the eloquent 
address and wise counsel of the Prince Consort. At one time a member 
of his household, it was my privilege to co-operate with this illustrious 
prince in many questions relating to the advancement of science. I 
naturally, therefore, turned to his presidential address to see whether I 
might not now continue those counsels which he then gave with all the 
breadth and comprehensiveness of his masterly speeches. I found, as I 
expected, a text for my own discourse in some pregnant remarks which 
he made upon the relation of Science to the State. They are as 
follows : — 'We may be justified in hoping . . . that the Legislature and 
the State will more and more recognise the claims of science to their 
attention, so that it may no longer require the begging-box, but speak to 
the State like a favoured child to its parent, sure of his paternal solicitude 
for its welfare ; that the State will recognise in science one of its elements 
of strength and prosperity, to foster which the clearest dictates of self- 
interest demand.' 

This opinion, in its broadest sense, means that the relations of science 
to the State should be made more intimate because the advance of science 
is needful to the public weal. 

The importance of promoting science as a duty of statecraft was well 
enough known to the ancients, especially to the Greeks and Arabs, but it 
ceased to be recognised in the dark ages, and was lost to sight during the 
revival of letters in the fifteenth and sixteenth centuries. Germany and 
France, which are now in such active competition in promoting science, 
have only publicly acknowledged its national importance in recent times. 
Even in the last century, though France had its Lavoisier and Germany 
its Leibnitz, their Governments did not know the value of science. When 
the former was condemned to deatli in the Reign of Terror, a petition was 
presented to the rulers that his life might be spared for a few weeks in 
order that he might complete some important experiments, but the reply 
was, ' The Republic has no need of savants.' Earlier in the century the 
much-praised Frederick William of Prussia shouted with a loud voice, 
during a graduation ceremony in the University of Frankfort, ' An ounce 
of mother-wit is worth a ton of university wisdom.' Both France and 
Germany are now ashamed of these utterances of their rulers, and make 
energetic eflbrts to advance science with the aid of their national resources. 
More remarkable is it to see a young nation like the United States reserv- 
ing large tracts of its national lands for the promotion of scientific 
education. In some respects this young country is in advance of all 



4 REPORT — 1885. 

together by the iron bands of railways from the Gulf of St. Lawrence to 
the PaciGc Ocean, so that the fertile lands of Ontario, Manitoba, Columbia, 
and the North- Western Territories will soon be available to the world. 
Still practical science has much to accomplish. England and France, 
with only one-fifth the fertile area of Canada, support 80 millions of 
people, while Canada has a population not exceeding 5 millions. 

A less far-seeing people than the Canadians might have invited the 
applied science which they so much require. But they knew that with- 
out science there are no applications. They no doubt felt with Emerson — 

And what if Trade sow cities 
Like shells along the shore, 
And thatch with towns the prairie broad 
M'ith railways ironed o'er ; 
They are but sailing foam-bells 
Along Thought's causing stream, 
And take their shape and sun-colour 
Yiom him that sends the dream. 

So it was with a far-reaching foresight that the Canadian Government 
invited the British Association for the Advancement of Science to meet 
in Montreal. The inhabitants of Canada received us with open arms, 
and the science of the Dominion and that of the United Kingdom were 
welded. We found in Canada, as Ave had every reason to expect, men of 
manly and self-reliant character who loved not less than we did the old 
home from whicli they had come. Among them is the same healthi- 
ness of political and moral life, with the same love of truth which dis- 
tinguishes the English people. Our great men are their great men ; our 
Shakspcare, !Milton, and Burns belong to them as much as to ourselves ; 
our Newton, Dalton, Faraday, and Darwin are their men of science as 
much as they are ours. Thus a common possession and mutual sympathy 
made the meeting in Canada a successful effort to stimulate the progress 
of science, while it established, at the same time, the principle that all 
people of British origin — and I would fain include our cousins in the 
United States — possess a common interest in the intellectual glories of 
their race, and ought, in science at least, to constitute part and parcel of 
a common empire, whose heart may beat in the small islands of the 
Northern seas, but whose blood circulates in all her limbs, carrying 
warmth to them and bringing back vigour to us. Nothing can be more 
cheering to our Association than to know that many of the young com- 
munities of English-speaking people all over the globe — in India, China, 
Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have 
founded scientific societies in order to promote the growth of scientific 
research. No doubt science, which is only a form of truth, is one in all 
lands, but still its unity of purpose and fulfilment received an important 
practical expression by our visit to Canada. This community of science 
will be continued by the fact that we have invited Sir William Dawson, 
of Montreal, to be our next President at Birmingham. 



ADDRESS. O 

II. Science and the State. 

1 cannot address you in Aberdeen without recollecting that when we 
last met in this city our President was a great prince. The just verdict 
of time is that, high as was his royal i-ank, he has a far nobler claim to 
our regard as a lover of humanity in its widest sense, and especially as a 
lover of those arts and sciences which do so much to adorn it. On 
September 14, 1859, I sat on this platform and listened to the eloquent 
address and wise counsel of the Prince Consort. At one time a member 
of his household, it was my privilege to co-operate with this illustrious 
prince in many questions relating to the advancement of science. I 
naturally, therefoi'e, turned to his presidential address to see whether I 
might not now continue those counsels which he then gave with all the 
breadth and comprehensiveness of his masterly speeches. I found, as I 
expected, a text for my own discourse in some pregnant remarks which 
he made upon the relation of Science to the State. They are as 
follows : — 'We may be justified in hoping . . . that the Legislature and 
the State will more and more recognise the claims of science to their 
attention, so that it may no longer require the begging-box, but speak to 
the State like a favoured child to its parent, sure of his paternal solicitude 
for its welfare ; that the State will recognise in science one of its elements 
of strength and prosperity, to foster which the clearest dictates of self- 
interest demand.' 

This opinion, in its broadest sense, means that the relations of science 
to the State should be made more intimate because the advance of science 
is needful to the public weal. 

The importance of promoting science as a duty of statecraft was well 
enough known to the ancients, especially to the Greeks and Arabs, but it 
ceased to be recosjuised in the dark a^es, and was lost to sigrht during the 
revival of letters in the fifteenth and sixteenth centuries. Germany and 
France, which are now in such active competition in promoting science, 
have only publicly acknowledged its national importance in recent times. 
Even in the last century, though France had its Lavoisier and Germany 
its Leibnitz, their Governments did not know the value of science. When 
the former was condemned to deatli in the Reign of Terror, a petition was 
presented to the rulers that his life might be spared for a few weeks in 
order that he might complete some important experiments, but the reply 
was, ' The Republic has no need of savants.' Earlier in the century the 
much-praised Frederick William of Prussia shouted with a loud voice, 
during a graduation ceremony in the University of Frankfort, ' An ounce 
of mother-wit is worth a ton of university wisdom.' Both France and 
Germany are now ashamed of these utterances of their rulers, and make 
energetic efforts to advance science with the aid of their national resources. 
More remarkable is it to see a young nation like the United States reserv- 
ing large tracts of its national lands for the promotion of scientific 
education. In some respects this young country is in advance of all 



6 ■ EEPORT 1885. 

Europoan nations in joining science to its administrative offices. Its 
scientific publications, like the great palteontological work embodying 
the researches of Professor Marsh and his associates in the Geological 
Survey, are an example to other Governments. The Minister of Agricul- 
ture is surrounded with a staff of botanists and chemists. The Home 
Secretary is aided by a special Scientific Commission to investigate the 
habits, migrations, and food of fishes, and the latter has at its disposal two 
specially-constrncted steamers of large tonnage. The United States and 
Gi'eat Britain i^i-omote fisheries on distinct systems. In this country we 
are perpetually issuing expensive Commissions to visit the coasts in order 
to ascertain the experiences of fishermen. I have acted as Chairman of one 
of these Royal Commissions, and found that the fishermen, having only a 
knowledge of a small area, gave the most contradictory and unsatisfactory- 
evidence. In America the questions are put to Nature, and not to fisher- 
men. Exact and searching investigations are made into the life-history 
of the fishes, into the temperature of the sea in which they live and 
spawn, into the nature of their food, and into the habits of their natural 
enemies. For this purpose the Government give the co-operation of the 
navy, and provide the Commission with a special corps of skilled naturalists, 
some of whom go out with the steamships and others work in the 
biological laboratories at Wood's Holl, Massachusetts, or at Washington. 
The difierent universities send their best naturalists to aid in these in- 
vestigations, which are under the direction of Mr. Baird, of the Smith- 
sonian Institution. The annual cost of the Federal Commission is about 
40,000/., while the separate States spend about 2O,O00Z. in local efibrts. 
The practical results flowing from these scientific investigations have 
been important. The inland waters and rivers have been stocked with 
fish of the best and most suitable kinds. Even the great ocean which 
washes the coasts of the United States is beginning to be afiected by the 
knowledge thus acquired, and a sensible result is already produced upon 
the most important of its fisheries. The United Kingdom largely depends 
upon its fisheries, but as j-et our Government have scarcely realised the 
value of such scientific investigations as those pursued with success by 
the United States. Less systematical!}', but with great benefit to science, 
our own Government has used the surveying expeditions, and sometimes 
has ec^uipped special expeditions to promote natural history and solar 
physics. Some of the latter, like the voyage of the ' Challenger,' have 
added largely to the store of knowledge ; while the former, though not 
primarily intended for scientific research, have had an indirect result 
of infinite value by becoming training-schools for such investigators 
as Edward Forbes, Darwin, Hooker, Huxley, Wyville Thomson, and 
others. 

In the United Kingdom we are just beginning to understand the 
wisdom of Washington's farewell address to his countrymen, when he said : 
' Promote as an object of primary importance institutions for the general 
diffusion of knowledge. In proportion as the structure of a governmeafc 



ADDRESS. 7 

gives force to public opinion, it is essential that public opinion should be 
enlightened.' It was only in 1870 that our Parliament established a 
system of national primary education. Secondary education is chaotic, 
and remains unconnected with the State, while the higher education of 
the universities is only brought at distant intervals under the view of the 
State. All great countries except England have Ministers of Education, 
but this country has only Ministers who are the managers of primary 
schools. We are inferior even to smaller countries in the absence of 
organised State supervision of education. Greece, Portugal, Egypt, and 
Japan have distinct Ministers of Education, and so also among our 
Colonies have Victoria and New Zealand . Gradually England is gathering 
materials for the establishment of an efficient Education Minister. The 
Department of Science and Art is doing excellent work in diffusino- 
a taste for elementary science among the working classes. There are 
now about 78,000 persons who annually come under the influence of its 
science classes, while a small number of about two hundied, many of them 
teachers, receive thorough instruction i"n science at the excellent school 
in South Kensington of which Professor Huxley is the Dean. I do not 
dwell on the work of this Government department, because my object ia 
chiefly to point out how it is that science lags in its progress in the United 
Kingdom owing to the deficient interest taken in it hj the middle and 
upper classes. The working classes are being roused from their indifi'er- 
ence. They show this by their selection of scientific men as candidates at 
the next election. Among these are Professors Stuart, Roscoe, Maskelyne, 
and Riicker. It has its significance that such a humble representative of 
science as myself received invitations from working-class constituencies 
in more than a dozen of the leading manufacturing towns. In the next 
Parliament I do not doubt that a Minister of Education will be created 
as a nucleus round which the various educational materials may crystallise 
in a definite form. 

III. Science and Secondary Education. 

Various Royal Commissions have made inquiries and issued recom- 
mendations in regard to our public and endowed schools. The Com- 
missions of I86I, 1804, 1868, and 1873 have expressed the strongest 
disapproval of the condition of our schools, and, so far as science is 
concerned, their state is much the same as when the Duke of Devon- 
shire's Commission in 1873 reported in the following words : — ' Con- 
sidering the increasing importance of science to the material interests of 
the country, we cannot but regard its almost total exclusion from the 
training of the upper and middle classes as little less than a national mis- 
fortune.' No doubt there are exceptional cases and some brilliant examples 
of improvement since these words were written, but generally throughout 
the country teaching in science is a name rather than a reality. The 
Technical Commission which reported last year can only point to three 
schools in Great Britain in which science is fully and adequately taught. 



8 REPORT 1885. 

While tbe Commission gives ns the consolation that England is still in 
advance as an industrial nation, it warns us that foreign nations, which 
were not long ago far behind, are now making more rapid progress than 
this country, and will soon pass it in the race of competition unless we 
give increased attention to science in public education. A few of the 
large towns, notably Manchester, Bradford, Hnddersfield, and Birming- 
ham, are doing so. The working classes are now receiving better 
instruction in science than the middle classes. The competition of 
actual life asserts its own conditions, for the children of the latter 6nd 
inci'easing difficulty in obtaining emjiloyment. The cause of this lies in 
the fact that the schools for the middle classes have not yet adapted 
themselves to tbe needs of modern life. It is true that many of the 
endowed schools have been put under new schemes, but as there is no 
public supervision or inspection of them, we have no knowledge as to 
whether they have prospered or slipped back. Many corporate schools 
have arisen, some of them, like Clifton, Cheltenham, and Marlborough 
Colleges, doing excellent educational work, though as regards all of them 
the public have no rights and cannot enforce guarantees for efficiency. 
A Return just issued, on the motion of Sir John Lubbock, shows a 
lamentable deficiency in science teaching in a great proportion of the 
endowed schools. While twelve to sixteen hours per week ars devoted to 
classics, two to three hours are considered ample for science in a large 
proportion of the schools. In Scotland there are only six schools in the 
Return which give more than two hours to science weekly, while in many 
schools its teaching is wholly omitted. Every other part of the kingdom 
stands in a better position than Scotland in relation to the science of its 
endowed schools. The old traditions of education stick as firmly to 
schools as a limpet does to a rock ; though I do the limpet injustice, for 
it does make excursions to seek pastui-es new. Are we to give up in 
despair because an exclusive system of classical education has resisted 
the assatilts of such cultivated authors as Milton, Montaigne, Cowley, and 
Locke ? There was once an enlightened Emperor of China, Chi Hwangti, 
who knew that his country was kept back by its exclusive devotion to the 
classics of Confucius and Mencius. He invited 500 of the teachers to 
bring their copies of these authors to Pekin, and after giving a great 
banquet in their honour, he buried alive the professors along with 
their manuscripts in a deep pit. But Confucius and j\Ienciu8 still reign 
supreme. I advocate milder measures, and depend for their adoption on 
the force of public opinion. The needs of modern life will force schools 
to adapt themselves to a scientific age. Grammar-schools believe them- 
selves to be immortal. Those curious immortals — the Struldbrugs — 
described by Swift, ultimately regretted their immortality, because they 
found themselves out of touch, sympathy, and fitness with the centuries 
in which they lived. 

As there is no use clamouring for an instrument of more compass and 
power until we have made up our mind as to the tune, Pi'ofessor Huxley, in 



ADDRESS. 9 

his evidence before a Parliamentary Committee in 1884, has given a time- 
table for grammar-schools. He demands that out of their forty hours 
for public and private study, ten should be given to modern languages and 
history, eight to arithmetic and mathematics, six to science, and two to 
geography, thus leaving fourteen hours to the dead languages. No time- 
table would, however, be suitable to all schools. The great public schools 
of England will continue to be the gymnasia for the upper classes, and 
should devote much of their time to classical and literary culture. Even 
now they introduce into their curriculum subjects unknown to them 
when the Royal Commission of 18G8 reported, though they still accept 
science with timidity. Unfortunately, the other grammar-schools which 
educate the middle classes look to the higher public schools as a type to 
which they should conform, although their functions are so different. 
It is in the interest of the higher public schools that this difference 
should be recognised, so that, while they give an all-round education and 
expand their curriculum by a freer recognition of the value of science as 
an educational power in developing the faculties of the upper classes, 
the schools for the middle classes should adapt themselves to the needs 
of their existence, and not keep up a slavish imitation of schools with a 
different function. 

The stock argument against the introduction of modern subjects into 
grammar-schools is that it is better to teach Latin and Greek thoroughly 
rather than various subjects less completely. But is it true that 
thoroughness in teaching dead languages is the result of an exclusive 
system ? In 1868 the Royal Commission stated that even in the few 
great public schools thoroughness was only given to thirty per cent, of 
the scholars, at the sacrifice of seventy per cent, who got little benefit 
from the system. Since then the curriculum has been widened and the 
teaching has improved. I question the soundness of the principle that it 
is better to limit the attention of the pupils mainly to Latin and Gi'eek, 
highly as I value their educational power to a certain order of minds. 
As in biology the bodily development of animals is from the general to 
the special, so is it in the mental development of man. In the school a 
boy should be aided to discover the class of knowledge that is best suited 
for his mental capacities, so that, in the upper forms of the school and in the 
university, knowledge maybe specialised in order to cultivate the powers 
of the man to their fullest extent. Shakspeare's educational formula 
may not be altogether true, but it contains a broad basis of truth — 

No profit grows, where is no pleasure ta'en ; — 
In brief, sii', study what you most affect. 

The comparative failure of the modern side of school education arises 
from constituting it out of the boys who are looked upon as classical 
asses. Milton pointed out that in all schools there are boys to whom the 
dead languages are ' like thorns and thistles,' which form a poor nourish, 
ment even for asses. If teachers looked upon these classical asses as 
beings who might receive mental nurture according to their nature, 



]0 REPORT — 1885. 

mucli higher results ■would follow the bifurcation of our schools. Saul 
•went out to look for asses and he found a kingdom. Surely this fact 
is more encouraging than the. example of Gideon, who ' took thorns of 
the wilderness and briars, and with these he taught the men of Succoth.' ' 
The adaptation of public schools to a scientific age does not involve 
a contest as to whether science or classics shall prevail, for both are 
indispensable to true education. The real question is whether schools 
will undertake the duty of moulding the minds of boys according to their 
mental varieties. Classics, from their structural perfection and power of 
awakening dormant faculties, have claims to precedence in education, 
but they have none to a practical monopoly. It is by claiming the latter 
that teachers sacrifice mental recepti^-ity to a Procrustean uniformity. 

The universities are changing their traditions more rapidly than the 
schools. The via antiqua which leads to them is still broad, though a 
via moderna, with branching avenues, is also open to their honours and 
emoluments. Physical science, which was once neglected, is now 
encouraged at the universities. As to the seventy per cent, of boys who 
leave schools for life-work without going through the universities, are 
there no growing signs of discontent which must force a change ? The 
Civil Sei'vice, the learned professions, as well as the armj^ and navy, are 
now barred by examinations. Do the boys of our public schools easily 
leap over the bars, although some of them have lately been lowered so as 
to suit the schools ? So difficult are these bars to scholars that crammers 
take them in hand before they attempt the leap ; and this occurs in spite 
of the large value attached to the dead languages and the small value 
placed on modern subjects. Thus, in the Indian Civil Service examina- 
tions, SOO marks as a maximum are assigned to Latin, GOO to Greek, 500 
to chemistry, and 300 to each of the other physical sciences. But if we 
take the average working of the system for the last four years, we find 
that while sixty-eight per cent, of the maximum were given to candidates 
in Greek and Latin, only forty-five pen' cent, were accorded to candidates in 
chemistry, and but thirty per cent, to the other physical sciences. Schools 
sending up boys for competition naturally shun subjects which are dealt 
"with so hardly and so heavily handicapped by the State. 

Passing from learned or public professions to commerce, how is it 
that in our great commercial centres, foreigners — German, Swiss, Dutch, 
and even Greeks — push aside our English youth and take the places of 
profit which belong to them by national inheritance ? How is it that in 
our Colonies, like those in South Africa, German enterprise is pushing 
aside English incapacity ? How is it that we find whole branches of 
manufactures, when they depend on scientific knowledge, passing away 
from this country, in which they originated, in order to engraft themselves 
abroad, although their decaying roots remain at home ? - The answer to 

' Judges viii. IG. 

- See Dr. Perkin.s' address to the Soc. Chem. Industry. 'Nature,' Aug. 6, 1885, 
p. 333. 



ADDRESS. 1 1 

tliese questions is that our systems of education are still too narrow for 
the increasing struggle of life. 

Faraday, who had no narrow vie\YS in regard to education, deplored 
the future of our youth in the competition of the world, because, as he 
said with sadness, ' our schoolboys, when they come out of school, are 
isrnorant of their ignorance at the end of all that education.' 

The opponents of science education allege that it is not adapted for 
mental development, because scientific facts are often disjointed and 
exercise only the memory. Those who argue thus do not know what 
science is. No doubt an ignorant or half-informed teacher may present 
science as an accumulation of unconnected facts. At all times and in all 
subjects there are teachers without a3sthetical or philosophical capacity 
— men who can only see carbonate of lime in a statue by Phidias or 
Praxiteles ; who cannot survey zoology on account of its millions of 
species, or botany because of its 130,000 distinct plants ; men who can look 
at trees without getting a conception of a forest, and cannot distinguish a 
stately edifice from its bricks. To teach in that fashion is like going to 
the tree of science with its glorious fruit in order to pick up a handful of 
the dry fallen leaves from the ground. It is, however, true that as 
science teaching has had less lengthened experience than that of literature, 
its methods of instruction are not so matured. Scientific and literary 
teaching have difiierent methods ; for while the teacher of literature rests 
on authority and on books for his guidance, the teacher of science 
discards authority and depends on facts at first hand, and on the book of 
Nature for their interpretation. Natural science more and more resolves 
itself into the teaching of the laboratory. In this way it can be used as 
a powerful means of quickening observation, and of creating a faculty of 
induction after the manner of Zadig, the Babylonian described by 
Voltaire. Thus facts become surrounded by scientific conceptions, and 
are subordinated to order and law. 

It is not those who desire to unite literature with science who degrade 
education ; the degradation is the consequence of the refusal. A violent 
reaction — too violent to be wise — has lately taken place against classical 
education in France, where their own vernacular occupies the position of 
dead languages, while Latin and science are given the same time in the 
curriculum. In England manufacturers cry out for technical education, 
in which classical culture shall be excluded. In the schools of the middle 
classes science rather than technics is needed, because, when the seeds of 
science are sown, technics as its fruit will appear at the appointed time. 
Epictetus was wise when he told us to observe that, though sheep eat 
grass, it is not grass but wool that grows on their backs. Should, how- 
ever, our grammar-schools persist in their refusal to adapt themselves to 
the needs of a scientific age, England must follow the example of other 
European nations and found new modern schools in competition with 
them. For, as Huxley has put it, we cannot continue in this age ' of full 
modern artillery to turn out our boys to do battle in it, equipped only 



12 KEPOET — 1885. 

with the sword and shield of an ancient gladiator.' In a scientific and 
keenly competitive age an exclusive education in the dead languages is 
a perplexing anomaly. The flowers of literature should be cultivated and 
gathered, though it is not wise to send men into our fields of industry to 
gather the harvest when they have been taught only to cull the poppies 
and to push aside the wheat. 

IV. Science and the Universities. 

The Stale has always felt bound to alter and improve universities, 
even when their endowments are so large as to render it unnecessary to 
support them by public funds. When universities are poor, Parliament 
gives aid to them from imperial taxation. In this country that aid has 
been given with a very spaiing hand. Thus the universities and colleges 
of Ireland have received about thirty thousand pounds annually, and tbo 
same sum has been granted to the four universities of Scotland. Com- 
pared Avith imperial aid to foreign universities such sums are small. A 
single German university like Strasburg or Leipsic receives above 
40,000Z. annually, or 10,000/. more than the whole colleges of Ireland or 
of Scotland. Strasburg, for instance, has had her university and its 
libraiy rebuilt at a cost of 711,000Z., and receives an annual subscription 
of 43,000Z. In rebuilding the university of Strasburg eight laboratories 
have been provided, so as to equip it fully with the modern requirements 
for teaching and reseai'ch.' Prussia, the most economical nation in the 
world, spends 391,000/. yearly out of taxation on her universities. 

The recent action of France is still more remarkable. After the 
Franco-German War the Institute of France discussed the important 
question : — ' Poui'quoi la France n'a pas trouve d'hommes superieurs au 
moment du \)(:v\\ ? ' The general answer was because France had allowed 
university education to sink to a low ebb. Before the great Revolution 
France had twenty-thi'ee autonomous universities in the provinces. 
Xapoleon desired to found one great university at Paris, and he crushed 
out the others with the hand of a despot, and remodelled the last with the 
instincts of a drill-sergeant. The central university sank so low that in 
1868 it is said that only 8,000/. were spent for true academic purposes. 
Startled by the intellectual sterility shown in the war, France has made 
gigantic eiforts to retrieve her position, and has rebuilt the provincial 
colleges at a cost of 3,280,000/., while her annual budget for their support 
now reaches half a million of pounds. In order to open these provincial 
colleges to the best talent of France, more than five hundred scholarships 
have been founded at an annual cost of 30,000/. France now recognises that 
it is not by the number of men under arms that she can compete with her 
great neighbour Germany, so she has determined to equal her in intellect. 

' The cost of these laboratories has been as follows : — Chemical Institute, 35,000Z. ; 
Physical Institute, 28,000Z. ; Botanical Institute, 2G,000Z. ; Observatory, 25,000?. ; 
Anatomy, 42,000/.; Clinical Surgery, 26,000/.; Physiological Chemistry, 16,000/.; 
Physiological Institute, 13,900/, 



ADDRESS. 13 

Tou will understand why it is that Germany was obliged, even if slie had 
not been willing, to spend sach large sums in order to equip the university 
of her conquered province, Alsace- Lorraine. France and Germany are 
fully aware that science is the source of wealth and power, and that the 
only way of advancing it is to encourage universities to make researches 
and to spread existing knowledge through the community. Other 
European nations are advancing on the same lines. Switzerland is a 
remarkable illustration of how a country can compensate itself for its 
natural disadvantages by a scientific education of its people. Switzerland 
contains neither coal nor the ordinary raw materials of industry, and is 
separated from other countries which might supply them by mountain 
barriers. Yet, by a singularly good system of graded schools, and by the 
great technical college of Ziirich, she has become a prosperous manufac- 
turing country. In Great Britain we have nothing comparable to thia 
technical college, either in magnitude or efScieucy. Belgium is reor- 
ganising its universities, and the State has freed the localities from the 
charge of buildings, and will in future equip the universities with efficient 
teaching resources out of public taxation. Holland, with a population of 
4,000,000 and a small revenue of 9,000,000/., spends 13G,O0OZ. on her 
four universities. Contrast this liberality of foreign countries in the 
promotion of higher instruction with the action of our own country. 
Scotland, like Holland, has four universities, and is not very different 
from it in population, but it only receives 30,000/. from the Slate. By a 
special clause in the Scotch Universities Bill the Governm_ent asked 
Parliament to declare that under no circumstances should the Parlia- 
mentary grant be ever increased above 40,000?. According to the views 
of the British Treasury there is a finality in science and in expandino- 
knowledge. 

The wealthy universities of Oxford and Cambridge are gradually con- 
structing laboratories for science. The merchant princes of Manchester 
have equipped their new Victoria University with similar laboratories. 
Edinburgh and Glasgow Universities have also done so, partly at the 
cost of Government and largely by private subscriptions. The poorer 
universities of Aberdeen and St. Andrews are still inefficiently provided 
with the modern appliances for teaching science. 

London has one small Government college and two chartered colleo-es, 
but is wholly destitute of a teaching university. It would excite o-reat 
astonishment at the Treasury if we were to make the modest request that 
the great metropolis, with a population of four millions, should be put 
into as efficient academical position as the town of Strasburg, with 
104,000 inhabitants, by receiving, as that town does, 43,000/. annually for 
academic instruction, and 700,000/. for university buildings. Still, the 
amazing anomaly that London has no teaching university must ere long 
cease. 

It is a comforting fact that, in spite of the indifference of Parliament, 
the large towns of the kingdom are showing their sense of the need of 



14 EEPOET — 1885. 

higher education. Manchester has already its university. Nottingham, 
Birmingham, Leeds, and Bristol have colleges more or less complete. 
Liverpool converts a disused lunatic asylum into a college for sane people. 
Cardiff rents an infirmary for a collegiate building. Dundee, by private 
benefaction, rears a Baxter College with larger ambitions. All these 
are healthy signs that the public are determined to have advanced science 
teachinc ; but the resources of the institutions are altogether inadequate 
to the end in view. Even in the few cases where the laboratories are effi- 
cient for teachino- purposes, they are inefficient as laboratories for research. 
Under these circumstances the Royal Commission on Science advocates 
special Government laboratories for research. Such laboratories, sup- 
ported by public money, are as legitimate subjects for expenditure as 
"alleries for pictures or sculpture ; but I think that they would not be 
successful, and would injure science if they failed. It would be safer in 
the meantime if the State assisted universities or well-established colleges 
to found laboratories of research under their own care. Even such a 
proposal shocks our Chancellor of the Exchequer, who tells us that this 
country is burdened with public debt, and has ironclads to build and 
arsenals to provide. Nevertheless our wealth is proportionally much 
greater than that of foreign States which are competing with so much 
vigour in the promotion of higher education. They deem such expenditure 
to be true economy, and do not allow their huge standing armies to be 
an apology for keeping their people backwards in the march of knowledge. 
France, which in the last ten years has been spending a million annually 
on university education, had a war indemnity to pay, and competes suc- 
cessfully with this country in ironclads. Either all foreign States are 
strano-ely deceived in their belief that the competition of the world has 
become a competition of intellect, or we are marvellously unobservant of J 
the change which is passing over Europe in the higher education of the ^ 
people. Preparations for war will not ensure to us the blessings and | 
security of an enlightened peace. Protective expenditure may be wise, 
thongh productive expenditure is wiser. 

Were half the powers which fill the worlrl with terror, 

AVere half the wealth bestowed on camps and courts, 

Given to redeem the human mind from error^ 

There were no need of arsenals and forts. 

Universities are not mere storehouses of knowledge ; they are also 
conservatories for its cultivation. In Mexico there is a species of ant which 
sets apart some of its individuals to act as honey-jars by monstrously 
extending their abdomens to store the precious fluid till it is wanted 
by the community. Professors in a university have a higher function, 
because they ought to make new honey as well as to store it. The 
widening of the bounds of knowledge, literary or scientific, is the crown- 
ino- o-lory of university life. Germany unites the functions of teaching 
and research in the universities, while France keeps them in separate 
institutions. The former system is best adapted to our habits, but its 



ADDRESS. 15 

condition for success is tliafc our science chairs should be greatly increased, 
so that teachers should not be wholly absorbed in the duties of instruc- 
tion. Germany subdivides the sciences into various chairs, and gives to 
the professors special laboratories. It also makes it a condition for the 
higher honours of a university that the candidates shall give proofs cf 
their ability to make original researches. Under such a system, teaching 
and investigation are not incompatible. In the evidence before the 
Science Commission many opinions were given that scientific men en- 
gaged in research should not be burdened with the duties of education, 
and there is much to be said in support of this view when a sino-le 
professor for the whole range of a physical science is its only represen- 
tative in a university. But I hope that such a system will not long 
continue, for if it do we must occupy a very inferiar position as a nation 
in the intellectual competition of Europe. Research and education in 
limited branches of higher knowledge are not incompatible. It is true 
that Gahleo complained of the burden imposed upon him by his numerous 
astronomical pupils, though few other philosophers have echoed this com- 
plaint. Newton, who produced order in worlds, and Dalton, who brought 
atoms under the reign of order and number, rejoiced in their pupils. 
Lalande spread astronomers as Liebig spread chemists, and Johannes 
Miiller biologists, all over the world. Laplace, La Grange, Dulong, 
Gay Lussac, Berthollet, and Dumas were professors as well as discoverers 
in France. In England our discoverers have generally been teachers. 
In fact I recollect only three notable examples of men who were not — 
Boyle, Cavendish, and Joule. It was so in ancient as well as in modern 
times, for Plato and Aristotle taught and philosophised. If you do not 
make the investigator a schoolmaster, as Dalton was, and as practically 
our professors are at the present time, with the duty of teaching all 
branches of their sciences, the mere elementary truths as well as the 
highest generalisations being compressed into a course, ifc is well that 
they should be brought into contact with the world in which they live, 
so as to know its wants and aspirations. They could then quicken the 
pregnant minds around them, and extend to others their own power and 
love of research. Goethe had a fine perception of this when he wrote — 

Wer in cTer Weltgeschichte lebt, 

Wer in die Zeiten schaut, und strebt, 

Nur der ist werth, zu sprechen und zu dichtcn. 

Our universities are still far from the attainment of a proper com- 
bination of their resources between teaching and research. Even Oxford 
and Cambridge, which have done so much in recent years in the equip- 
ment of laboratories and in adding to their scientific stafP, are still far 
behind a second-class German university. The professional faculties of 
the English universities are growing, and will dififuse a greater taste for 
science among their students, though they may absorb the time of the 
limited professoriate so as to prevent it advancing the boundaries of 



16 REPORT — 1885. 

knowledo-e. Professional faculties are absolutely essential to tbe existence 
of universities in poor countries like Scotland and Ireland. This L.is 
been the case from the early days of the Bologna University up to the 
present time. Originally universities arose not by mere bulls of popes, 
but as a response to the strong desire of the professional classes to dignify 
their crafts by real knowledge. If their education had been limited to 
mere technical schools like the Medical School of Salerno which flourished 
in the eleventh century, length but not breadth would have been given to 
education. So the universities wisely joined culture to the professional 
ociences. Poor countries like Scotland and Ireland must have their 
academic systems based on the professional faculties, although wealthy 
universities like Oxford and Cambridge may continue to have them as 
mere supplements to a more general education. A greater liberality 
of support on the part of the State in the establishment of chairs of 
science, for the sake of science and not merely for the teaching of the 
professions, would enable the poorer universities to take their part in the 
advancement of knowledge. 

I have already alluded to the foundation of new colleges in different 
parts of the kingdom. Owens College has worthily developed into the 
Victoria University. Formerly she depended for degrees on the 
University of London. No longer will she be like a moon reflecting cold 
and sickly rays from a distant luminary, for in future she will be a sun, 
a centre of intelligence, warming and illuminating the regions around her. 
The other colleges which have formed themselves in large manufacturing 
districts are remarkable expressions from them that science must be 
promoted. Including the colleges of a high class, such as University 
College and King's College in London, and the three Queen's Colleges in 
Ireland, the aggregate attendance of students in colleges without university 
rank is between nine and ten thousand, while that of the universities is 
fifteen thousand. No doubt some of the provincial colleges require 
considerable improvement in their teaching methods; sometimes they 
unwisely aim at a full university curriculum when it would be better for 
them to act as faculties. Still they are all growing in the spirit of self- 
help, and some of them are destined, like Owens College, to develop into 
universities. This is not a subject of alarm to lovers of education, 
while it is one of hope and encouragement to the great centres of 
industry. There are too few autonomous universities in England in 
proportion to its population. "While Scotland, with a population 
of 3J millions, has four universities with 6,500 students, England, 
with 26 millions of people, has only the same number of teaching 
universities with 6,000 students. Unless English colleges have such 
ambition, they may be turned into mere mills to grind out material for 
examinations and competitions. Higher colleges should always hold 
before their students that knowledge, for its own sake, is the only object 
worthy of reverence. Beyond college life there is a land of research 
flowing with milk and honey for those who know how to cultivate it. 



ADDRESS. 1 1 

Colleges should at least show a Pisgah view of this Land of Promise, 
which stretches far beyond the Jordan of examinations and competitions. 

V. Science and Inclustnj, 

In the popular mind the value of science is measured by its applica- 
tions to the useful purposes of life. It is no doubt true that science 
wears a beautiful aspect when she confers practical benefits upon man. 
But truer relations of science to industry are implied in Greek mythology. 
Vulcan, the god of industry, wooed science, in the form of Minerva, with 
a passionate love, but the chaste goddess never married, although she 
conferi'ed upon mankind nearly as many arts as Prometheus, who, like 
other inventors, saw civilisation progressing by their use while he lay 
groaning in want on Mount Caucasus. The rapid development of industry 
in modern days depends on the applications of scientific knowledge, 
while its slower growth in former times was due to experiments being 
made by trial and error in order to gratify the needs of man. Then an 
experiment was less a questioning of Nature than an exercise on the mind 
of the experimentalist. For a true questioning of Nature only arises when 
intellectual conceptions of the causes of phenomena attach themselves to 
ascertained facts as well as to their natural environments. Much real 
science had at one time accumulated in Egypt, Greece, Rome, and Arabia, 
though it became obscured by the intellectual darkness which spread 
over Europe like a pall for many centuries. The mental results of Greek 
science, filtered through the Romans and Arabians, gradually fertilised 
the soil of Europe. Even in ages which are deemed to be dark and un- 
prolific, substantial though slow progress was made. By the end of the 
fifteenth century the mathematics of the Alexandrian school had become 
the possession of Western Europe ; Arabic numerals, algebra, trigo- 
nometry, decimal reckoning, and an improved calendar having been 
added to its stock of knowledgre. The old discoveries of Democritus and 
Archimedes in physics, and of Hipparchus and Ptolemy in astronomy, 
were producing their natural developments, though with great slowness. 
Many manufactui'es, growing chiefly by experience, and occasionally 
lightened up by glimmerings of science throughout the prevailing dark- 
ness, had arisen before the sixteenth century. A knowledge of the pro- 
perties of bodies, though scarcely of their relations to each other, came 
through the labours of the alchemists, who had a mighty impulse to 
work, for by the philosopher's stone, often not larger than half a rape- 
seed, they hoped to attain the three sensuous conditions of human enjoy- 
ment, gold, health, and immortality. By the end of the fifteenth century 
many important manufactures were founded by empirical experiment, 
with only the uncertain guidance of science. Among these were the 
compass, printing, paper, gunpowder, guns, watches, forks, knitting- 
needles, horseshoes, bells, wood cutting and copper engraving, wire- 
drawing, steel, table glass, spectacles, mici-oscopes, glass mirrors backed 
by amalgams of tin and lead, windmills, crushing and saw mills. These 

1885. c 



18 REPora- — 1835. 

important manufactures arose from an increased knowledge of facts, 
around whicli scientific conceptions were slowly concreting. Aristotle 
defines this as science when he says, ' Art begins when, from a great 
number of experiences, one genei'al conception is formed which will 
embrace all similar cases.' Such conceptions are formed only when 
culture develops the human mind and compels it to give a rational 
account of the world in which man lives, and of the objects in and around 
it, as well as of the phenomena which govern their action and evolution. 
Though the accumulation of facts is indispensable to the growtb of science, 
a thousand facts are of less value to human progress than is a single one 
when it is scientifically comprehended, for it then becomes generalised in all 
similar cases. Isolated facts may be viewed as the dust of science. The dust 
which floats in the atmosphere is to the common observer mere incoherent 
matter in a wrong place, while to the man of science it is all-important 
when the rays of heat and light act upon its floating particles. It is by 
them that clouds and rains are influenced ; it is by their selective influence 
on the solar waves that the blue of the heavens and the beauteous colours 
of the sky glorify all Nature. So, also, ascertained though isolated facts, 
forming the dust of science, become th.e reflecting media of the light of 
knowledge, and cause all Nature to assume a new a.spect. It is with the 
light of knowledge that we are enabled to question Nature through direct 
experiment. The hypothesis or theory which induces us to put tlie ex- 
perimental question maybe right or wrong; still, ^)-?(c?e>is qiiestio dimidium 
scienticB est — it is half way to knowledge when you know what you have 
to inquire. Davy described hypothesis as the mere scafiblding of science, 
useful to build up true knowledge, but capable of being put up or taken 
down at pleasure. Undoubtedly a theory is only temporary, and the 
reason is, as Bacon has said, that the man of science ' loveth truth more 
than his theory.' The changing theories which the world despises are 
the leaves of the tree of science drawing nutriment to the parent stems, 
and enabling it to put forth new branches and to produce f I'uit ; and 
though the leaves fall and decay, the very products of decay nourish the 
roots of the tree and reappear in the new leaves or theories which succeed. 
When the questioning of Nature by intelligent experiment has raised 
a system of science, then those men who desire to apply it to industrial 
inventions proceed by the same methods to make rapid progress in the 
arts. They also must have means to compel Nature to reveal her secrets, 
^neas succeeded in his great enterprise by plucking a golden branch 
from the tree of science. Armed with this even dread Charon dared not 
refuse a passage across the Styx ; and the gate of the Elysian fields was 
unbarred when he hung the branch on its portal. Then new aspects of 
Nature were revealed — 

Another sun and stars they know 
That shine like ours, but shine below. 

It is by carrying such a golden branch from the tree of science that in- 



ADDEESS. 1 9 

rentors are able to advance the arts. In illustration of bow slowly at 
first and bow rapidly afterwards science and its applications arise, I will 
take only two out of thousands of examples which lie ready to my hand. 
One of the most familiar instances is air, for that surely should have been 
soon understood if man's unaided senses are sufficient for knowledge. Air 
has been under the notice of mankind ever since the first man drew bis 
first breath. It meets him at every turn ; it fans him with gentle breezes, 
and it buffets him with storms. And yet it is certain that this familiar 
object — air — is very imperfectly understood up to the present time. We 
now know by recent researches that air can be liquefied by pressure and 
cold ; but as a child still looks upon air as nothing, so did man in his 
early state. A vessel filled with air was deemed to be empty. But man, 
as soon as he began to speculate, felt the importance of air, and deemed 
it to be a soul of the world upon which the respiration of man and the 
god-like quality of fire depended. Yet a really intelligent conception of 
these two essential conditions to man's existence — respiration and com- 
bustion — was not formed till about a century ago (1 775). No doubt long 
before that time there had been abundant speculations regarding air. 
Anaximenes, 548 years before Christ, and Diogenes of Apollonia, a century 
later, studied the properties of air so far as their senses would allow them ; 
so, in fact, did Aristotle. Actual scientific experiments were made on air 
about the year 1100 by a remarkable Saracen, Alhazen, who ascertained 
important truths which enabled Galileo, Torricelli, Otto de Guericke, and 
others at a later period to discover laws leading to important practical 
applications. Still there was no intelligent conception as to the compo- 
sition of air until Priestley in 1774 i*epeated, with the light of science, an 
empirical observation which Eck de Sulbach had made three hundred 
years before upon the union of mercury with an ingredient of air and the 
decomposition of this compound by heat. This experiment now proved 
that the active element in air is oxygen. From that date our knowledge, 
derived from an intelligent questioning of air by direct experiments, has 
gone on by leaps and bounds. The air, which mainly consists of nitrogen 
and oxygen, is now known to contain carbonic acid, ammonia, nitric acid, 
ozone, besides hosts of living organisms which have a vast influence for 
good or evil in the economy of the world. These micro-organisms, the 
latest contribution to our knowledge of air, perform great analytical 
functions in organic nature, and are the means of converting much of its 
potential energy into actual energy. Through their action on dead matter 
the mutual dependence of plants and animals is secured, so that the air 
becomes at once the grave of organic death and the cradle of organic life. 
No doubt the ancients suspected this without being able to prove the de- 
pendence. Euripides seems to have seen it deductively when he describes 
the results of decay : — 

Then that which springs from earth, to earth returns, 
And that which draws its being from the sky 
Eises again up to the skyey height 

C 2 



20 REPORT — 1885. 

Tlie consequences of the progressive discoveries have added largely to 
our knowledge of life, and have given a marvellous development to the 
industrial arts. Combustion and respiration govern a wide range of 
processes. The economical use of fuel, the growth of plants, the food of 
animals, the processes of husbandry, the maintenance of public health, 
the orio-in and cure of disease, the production of alcoholic drinks, the 
processes of making vinegar and saltpetre — all these and many other 
kinds of knowied"-e have been brought under the dominion of law. No 
doubt animals respired, fuel burned, plants grew, sugar fermented, before 
Tve knew how they depended upon air. But as the knowledge was 
empirical, it could not be intelligently directed. Now all these processes 
are ranched in order under a wise economy of Nature, and can be directed 
to the utilities of life ; for it is trup, as Swedenborg says, that ' human 
ends always ascend as Nature descends.' There is scarcely a large 
industry in the world which has not received a mighty impulse by the 
better knowledge of air acquired within a hundred years. If I had time 
I could show still more strikingly the industrial advantages which have 
followed from Cavendish's discovery of the composition of water. I wish 
that I could have done this, because it was Addison who foolishly said, 
and Paley who as unwisely approved the remark, ' that mankind required 
to know no more about water than the temperature at which it froze and 
boiled, and the mode of making steam.' 

"When we examine the order of progress in the arts, even before they 
are illumined by science, their improvements seem to be the resultants of 
three conditions. 

1. The substitution of natural forces for brute aiiimal power, as 
when Hercules used the waters of the Alpheus to cleanse the Augean 
stables; or when a Kamchadal of Eastern Asia, who has been three 
years hollowing out a canoe, finds that he can do it in a few hours by 

fire. 

2. The economy of time, as when a calendering machine produces 
the same gloss to miles of calico that an African savage gives to a few 
inches by rubbing it with the shell of a snail ; or the economy of produc- 
tion, as when steel pens, sold when first introduced at one shilling apiece, 
are now sold at a penny per dozen ; or when steel rails, lately costing 
45Z. per ton, can now be sold at 5/. 

3. Methods of utilising waste products, or of endowing them with 
properties which render them of increased valae to industry, as when 
waste scrap iron and the galls on the oak are converted into ink ; or the 
badly-smelling waste of gasworks is transformed into fragrant essences, 
brilliant dyes, and fertilising manure ; or when the efl'ete matter of 
animals or old bones is changed into lucifcr-matches. 

All three results are often combined when a single end is obtained — 
at all events, economy of time and production invariably follows when 
natural forces substitute brute animal force. In industrial progress the 
sweat of the brow is lessened by the conceptions of the brain. How 



ADDRESS. 21 

exultant is the old Greek poet, Antipater,' when women are relieved of 
the drudgery of turning the grindstones for the daily supply of corn. 
' Woman ! you who have hitherto had to grind corn, let your arms rest 
for the future. It is no longer for you that the birds announce by their 
songs the dawn of the morning. Ceres has ordered the loater-nymplis to 
move the heavy millstones and perform your labour.' Penelope had 
twelve slaves to grind corn for her small household. During the most 
prosperous time of Athens it was estimated that there were twenty slaves 
to each free citizen. Slaves are mere machines, and machines neither 
invent nor discover. The bondmen of the Jews, the helots of Sparta, 
the captive slaves of Rome, the serfs of Europe, and uneducated labourers 
of the present day who are the slaves of ignorance have added nothing 
to human progress. But as natural forces substitute and become cheaper 
than slave labour, liberty follows advancing civilisation. Machines 
require educated superintendence. One shoe factory in Boston by its 
machines does the work of thirty thousand shoemakers in Paris who 
have still to go through the weary drudgery of mechanical labour. The 
steam power of the world, during the last twenty years, has risen from 
11^ million to 29 million horse-power, or 152 per cent. 

Let me take a single example of how even a petty manufacture improved 
by the teachings of science affects the comforts and enlarges the resources 
of mankind. When I was a boy, the only way of obtaining a light 
was by the tinder-box, with its quadruple materials, flint and steel, burnt 
rags or tinder, and a sulphur-match. If everything went well, if the box 
could be found and the air was dry, a light could be obtained in two 
minutes ; but xerj often the time occupied was much longer, and the 
process became a great trial to the serenity of temper. The consequence 
of this was that a fire or a burning lamp was kept alight through the 
day. Old Gerard, in his Herbal, tells us how certain fungi were used to 
carry fire from one part of the country to the other. The tinder-box 
long held its position as a great discovery in the arts. The Pyxidicula 
Igniaria of the Romans appears to have been much the same implement 
as, though a little ruder than, the flint and steel which Philip the Good 
put into the collar of the Golden Fleece in 1429 as a representation of 
high knowledge in the progress of the arts. It continued to prevail 
till 1833, when phosphorus-matches were introduced ; though I have been 
amused to find that there are a few venerable ancients in London who 
still stick to the tinder-box, and for whom a few shops keep a small 
supply. Phosphorus was no new discovery, for it had been obtained by 
an Arabian called Bechel in the eighth century. However, it was for- 
gotten, and was rediscovered by Brandt, who made it out of very 
stinking materials in 1G69. Other discoveries had, however, to be 
made before it could be used for lucifer-matches. The science of com- 
bustion was only developed on the discovery of oxygen a century later. 
Time had to elapse before chemical analysis showed the kind of bodies 

' Analecta Veterum Gracorum, Epig. 39, vol. ii. p. 119. 



22 EEroiiT — 1885. 

■whicli could be added to phosphorus so as to make it ignite readily. So 
it Tvas not till 1833 that matches became a partial success. Intolerably 
bad they then were, dangerously inflammable, horribly poisonous to the 
makers and injurious to the lungs of the consumers. It required another 
discovery by Schrotter in 1845 to change poisonous waxy into innocuous 
red-brick phosphorus in order that these defects might be remedied, and 
to give us the safety-match of the present day. Now what have these 
successive discoveries in science done for the nation, in this single manu- 
facture, by an economy of time ? If before 1833 we had made the same 
demands for light that we now do, when we daily consume eight matches 
per head of the population, the tinder-box could have sujjplied the de- 
mand under the most favourable conditions by an expenditure of one 
quarter of an hour. The lucifer-match supplies a light in fifteen seconds 
on each occasion, or in two minutes for the whole day. Putting these 
differences into a year, the venerable ancient who still sticks to his 
tinder-box would require to spend ninety hours yearly in the production 
of light, while the user of lucifer-matches spends twelve hours; so that 
the latter has an economy of seventy-eight hours yearly, or about ten 
working days. Measured by cost of production at one shilling and six- 
pence daily, the economy of time represented in money to our population is 
twenty-six millions of pounds annually. This is a curious instance of the 
manner in which science leads to economy of time and wealth even in a 
small manufacture. In larger industries the economy of time and labour 
produced by the application of scientific discoveries is beyond all measure- 
ment. Thus the discovery of latent heat by Black led to the inventions 
of Watt ; while that of the mechanical equivalent of heat by Joule has 
been the basis of the progressive improvements in the steam-engine which 
enables power to be obtained by a consumption of fuel less than one- 
fourth the amount used twenty years ago. It may be that the engines of 
Watt and Stephenson will yield in their turn to more economical motors ; 
still they have already expanded the wealth, resources, and even the terri- 
tories of England more than all the battles fought by her soldiers or all 
the treaties negotiated by her diplomatists. 

The coal which has hitherto been the chief soTirce of power probably re- 
presents the product of five or six million years during which the sun shone 
upon the plants of the Carboniferous Period, and stored up its energy in this 
convenient form. But we are using this conserved force wastefuUy and 
prodigally ; for, although horse-power in steam engines has so largely in- 
creased since 1864, two men only now produce what three men did at 
that date. It is only three hundred years since we became a manufactur- 
ing country. According to Professor Dewar, in less than two hundred 
years more the coal of this country will be wholly exhausted, and in half 
that time will be difficult to procure. Our not very distant descendants 
will have to face the problem — What will be the condition of England 
without coal ? The answer to that question depends u^dou the intel- 
lectual development of the nation at that time. The value of the in- 



ADDEESS. 23 

tellcctual factor of production is continually increasing ; wliilc the values 
of rav,' material and fuel are lessening factors. It may be that when tlie 
dreaded time of exhansted fuel Las arrived, its importation from other 
coal-fields, such as those of New South Wales, will be so easy and cheap 
that the increased technical education of our operatives may largely over- 
balance the disadvantages of increased cost in fuel. But this supposes 
that future Governments in England will have more enlightened views as 
to the value of science than past Governments have possessed. 

Industrial applications are but the overflowings of science welling 
over from the fulness of its measnre. Few would ask now, as was con- 
stantly done a few years ago, ' What is the use of an abstract discovery 
in science ? ' Faraday once answered this question by another, ' What 
is the use of a baby ? ' Yet round that baby centre all the hopes and 
sentiments of his parents, and even the interests of the State, which 
interferes in its upbringing so as to ensure it being a capable citizen. 
The pi-ocesses of mind which produce a discovery or an invention are 
rarely associated in the same person, for while the discoverer seeks to 
explain causes and the relations of phenomena, the inventor aims at pro- 
ducing new effects, or at least of obtaining them in a novel and efficient 
way. In this the inventor may sometimes succeed without much know- 
ledge of science, though his labours are infinitely more productive when 
he understands the causes of the effects which he desires to produce. 

A nation in its industrial progress, when the competition of the world 
is keen, cannot stand still. Three conditions only are possible for it. It 
may go forward, retrogi-ade, or perish. Its extinction as a great nation 
follows its neglect of higher education, for, as described in the proverb of 
Solomon, ' They that hate instruction love death.' In sociology, as in 
biology, there are three states. The first of balance, when things grow 
neither better nor worse ; the second that of elaboration or evolution, as 
we see it when animals adapt themselves to their environments ; and the 
third, that of degeneration, when they rapidly lose the ground they have 
made. For a nation, a state of balance is only possible in the early stage 
of its existence, but it is impossible when its environments are constantly 
changing. 

The possession of the raw materials of industry and the existence of a 
surplus population are important factors for the growth of manufactures 
in the early history of a nation, but afterwards they are bound up with 
another factor — -the application of intellect to their development. England 
could not be called a manufacturing nation till the Elizabethan age. No 
■doubt coal, iron, and wool were in abundance, though, in the reign of 
the Plantagenets, they produced little pi'osperity. Wool was sent to 
Flanders to be manufactured, for England then stood to Holland as 
Australia now does to Yorkshire. The political crimes of Spain from the 
reign of Ferdinand and Isabella to that of Philip HI. destroyed it as a 
great manufacturing nation, and indirectly led to England taking its 
position. Spain, through the activity and science of the Arabian intellect, 



24 EBPORT — 1885. 

bad acquired many important industries. The Moors and the Moriscoes, 
who had been in Spain for a period as long as from the Norman 
Conquest of this country to the present date, were banished, and with 
them departed the intellect of Spain. Then the invasion of the Low 
Countries by Philip II. drove the Flemish manufacturers to England, 
while the French persecution of the Huguenots added new manufacturing 
experience, and with them came the industries of cotton, wool, and silk. 
Cotton mixed with linen and wool became freely used, but it was only from 
1738 to the end of the century that the inventions of Wyatt, Arkwright, 
Hargreaves, Crompton, and Cartwright started the wonderful modern 
development. The raw cotton was imported from India or America, but 
that fact as regards cost was a small factor in comparison with the intellect 
required to convert it into a utility. Science has in the last hundred 
years altered altogether the old conditions of industrial competition. She 
has taught the rigid metals to convey and record our thoughts even to 
the most distant lands, and, within less limits, to reproduce our speech. 
This mai'vellous application of electricity has diminished the cares and 
responsibilities of Governments, while it has at the same time altered the 
whole practice of commerce. To England steam and electricity have 
been of incalculable advantage. The ocean, which once made the coun- 
try insular and isolated, is now the very life-blood of England and of 
the greater England beyond the seas. As in the human body the blood 
bathes all its parts, and through its travelling corpuscles carries force to 
all its members, so in the body politic of England and its pelagic exten- 
sions, steam has become the circulatory and electricity the nervous 
system. The colonies, being young countries, value their raw materials as 
their chief sources of wealth. "When they become older they will dis- 
cover it is not in these, but in the cultui'e of scientific intellect, that their 
future prosperity depends. Older nations recognise this as the law of 
progress more than we do ; or, as Jules Simon tersely puts it — ' That 
nation which most educates her people will become the greatest nation, 
if not to-day, certainly to-morrow.' Higher education is the condition of 
higher prosperity, and the nation which neglects to develop the intel- 
lectual factor of production must degenerate, for it cannot stand still. 
If we felt compelled to adopt the test of science given by Comte, that its 
value must be measured by fecundity, it might be prudent to claim indus- 
trial inventions as the immediate fruit of the tree of science, though only 
fruit which the prolific tree has shed. But the test is untrue in the sense 
indicated, or rather the fruit, according to the simile of Bacon, is like the 
golden apples which Aphrodite gave to the suitor of Atalanta, who lagged 
in her course by stooping to pick them up, and so lost the race. The 
true cultivators of the tree of science must seek their own reward by 
seeing it flourish, and let others devote their attention to the possible 
practical advantages which may result from their labours. 

There is, however, one intimate connection between science and in- 
dustry which I hope will be more intimate as scientific education becomes 



ADDRESS. 25 

more prevalent in our scliools and universities. Abstract science depends 
on the support of men of leisure, either themselves possessing or having 
provided for them the means of living without entering into the pursuits 
of active industry. The pursuit of science requires a superfluity of wealth 
in a community beyond the needs of ordinary life. Such superfluity is 
also necessary for art, though a picture or a statue is a saleable commodity, 
while an abstract discovery in science has no immediate or, as regards 
the discoverer, proximate commercial value. In Greece, when philo- 
sophical and scientific speculation was at its highest pomt, and when 
education was conducted in its own vernacular and not through dead 
languages, science, industry, and commerce wei-e actively prosperous. 
Corinth carried on the manufactures of Birmingham and Sheffield, while 
Athens combined those of Leeds, Staffordshire, and London, for it had 
■woollen manufactures, potteries, gold and silver work, as well as ship- 
building. Their philosophers were the sons of biarghers, and sometimes 
carried on the trades of their fathers. Thales was a travelling oil 
merchant, who brought back science as well as oil from Egypt. Solon 
and his great descendant Plato, as well as Zeno, were men of commerce. 
Socrates was a stone-mason ; Thucydides a gold-miner ; Aristotle kept a 
druggist's shop until Alexander endowed him with the wealth of Asia. 
All but Socrates had a superfluity of wealth, and he was supported by 
that of others. Now if our universities and schools created that love 
of science which a broad education would surely inspire, our men of 
riches and leisure who advance the boundaries of scientific knowledge 
could not be counted on the fingers as they now are, when we think of 
Boyle, Cavendish, Napier, Lyell, Murchison, and Darwin, but would be as 
numerous as our statesmen and orators. Statesmen, without a following 
of the people who share their views and back their work, would be feeble 
indeed. But while England has never lacked leaders in science, they have 
too few followers to risk a rapid march. We might create an army to 
support our generals in science, as Germany has done, and as France is now 
doing, if education in this country would only m.ould itself to the needs 
of a scientific age. It is with this feeling that Horace Mann wrote :— ' The 
action of the mind is like the action of fire ; one billet of wood will hardly 
burn alone, though as dry as the sun and north-west wind can make it, 
and though placed in a current of air ; ten such billets will burn well 
together, but a hundred will create a heat fifty times as intense as ten — 
will make a current of air to fan their own flame, and consume even 
greenness itself.' 

VI. Abstract Science the Condition for Progress. 

The subject of my address has been the relations of science to the public 
weal. That is a very old subject to select for the year 1885. I began it 
by quoting the words of an illustrious prince, the consort of our Queen, 
who addressed us on the same subject from this platform twenty-six 
years ago. But he was not the first prince who saw how closely science 



26 REPORT — 1885. 

is bound uj^ with the Avelfare of States. AH, the son-in-law of Mahomet, 
the fourth successor to the Caliphate, urged upon his followers that men 
of science and their disciples give security to human progress. Ali loved 
to say, ' Eminence in science is the highest of honours,' and ' He dies not 
who gives life to learning.' In addressing you upon texts such as these, 
my purpose was to show how unwise it is for England to lag in the 
onward march of science when most other European Powers are using 
the resources of their States to promote higher education and to advance 
the boundaries of knowledge. English Governments alone fail to grasp 
the fact that the competition of the world has become a competition in 
intellect. !Much of this indifierence is due to our systems of education. 
I have ill fulfilled my purpose if, in claiming for science a larger share in 
public education, I have in any way depreciated literature, art, or philo- 
sophy, for every subject which adds to culture aids in human develop- 
ment. I only contend that in public education thei-e should be a free 
play to the scientific faculty, so that the youths who possess it should 
leai-n the richness of their possession during the educative process. The 
same faculties which make a man great in any walk of life — strong love 
of truth, high imagination tempered by judgment, a vivid memory which 
can co-ordinate other facts with those under immediate consideration— all 
these are qualities which the poet, the philosopher, the man of literature, 
and the man of science equally require and should cultivate through all 
parts of their education as well as in their future careers. My contention 
is that science should not be practically shut out from the view of a youth 
while his education is in progress, for the public weal requires that 
a large number of scientific men should belong to the community. This 
is necessary- because science has impressed its character upon the age in 
which we live, and as science is not stationary but progressive, men are re- 
quired to advance its boundaries, acting as pioneers in the onward march 
of States. Human progress is so identified with scientific thought, both 
in its conception and realisation, that it seems as if they were alternative 
terms in the history of civilisation. In literature, and even in art, a 
standard of excellence has been attained which we are content to imitate 
because we have been unable to surpass. But there is no such standard 
in science. Formerly, when the dark cloud was being dissipated which 
had obscured the learning of Gi-eece and Rome, the diffusion of literature 
or the discovery of lost authors had a marked influence on advancing 
civilisation. Now, a Chrysoloras might teach Greek in the Italian uni- 
versities without hastening sensibly the onward march of Italy ; a 
Poggio might discover copies of Lucretius and Quintilian without 
exercising a tithe of the influence on modern life that an invention by 
Stephenson or Wheatstone would produce. Nevertheless, the divorce of 
culture and science, which the present state of education in this country 
tends to produce, is deeply to be deplored, because a cultured intelligence 
adds greatly to the development of the scientific faculty. My argument 
is that no amount of learning without science suffices in the present state 



ADDRESS. 27 

of the world to put us in a position wliicli will enable England to keep 
ahead or even on a level with foreign nations as regards knowledge and 
its applications to the utilities of life. Take the example of any man of 
learning, and see how soon the direct consequences resulting from his 
learning disappear in the life of a nation, while the discoveries of a man 
of science remain productive amid all the shocks of empire. As 1 am in 
Aberdeen I remember that the learned Dutchman Erasmus was intro- 
duced to England by the encouragement which he received from Hector 
Boece, the Principal of King's College in this University. Yet even in 
the case of Erasmus — who taught Greek at Cambridge and did so much 
for the revival of classical literature as well as in the promotion of spiritual 
freedom — how little has civilisation to ascribe to him in comparison with 
the discoveries of two other Cambridge men, Newton and Cavendish. 
The discoveries of Newton will influence the destinies of mankind to the 
end of the world. "When he established the laws by which the motions 
of .the great masses of matter in the universe are governed, he con- 
ferred an incalculable benefit upon the intellectual development of the 
human race. No gi-eat discovery flashes upon the world at once, and 
therefore Pope's lines on Newton are only a poetic fancy : — 

Nature and Nature'.s laws laj' hid in night, 
God said, ' Let Newton be,' and all was liglit. 

No doubt the road upon which he travelled had been long in preparation 
by other men. The exact observations of Tycho Brahe, coupled with the 
discoveries of Copernicus, Kepler, and Galileo, had already broken down 
the authority of Aristotle and weakened that of the Church. But though 
the conceptions of the universe were thus broadened, mankind had not 
yet rid themselves of the idea that the powers of the universe were still 
regulated by spirits or special providences. Even Kepler moved the 
planets by spirits, and it took some time to knock these celestial steers- 
men on the head. Descartes, who really did so much by his writings to 
force the conclusion that the planetary movements should be dealt with 
as an ordinary problem in mechanics, looked upon the universe as a 
machine, the wheels of which were kept in motion by the unceasing 
exercise of a divine power. Yet such theories were only an attempt to 
regulate the universe by celestial intelligences like our own, and by 
standards within our reach. It required the discovery of an all-pervading 
law, universal thi-oughout all space, to enlarge the thoughts of men, and 
one which, while it widened the conceptions of the universe, reduced the 
earth and solar system to true dimensions. It is by the investigation of 
the finite on all sides that we obtain a higher conception of the infinite — 

Willst du ins TJnendliche sclireiten, 
Geh nur im Endlichen nach alien Seiten. 

Ecclesiastical authority had been already undermined by earnest inquirers 
such as Wycliffe and Huss before Luther shook the pillars of the Vatican. 



28 REPORT — 1885. 

They were removers of abuses, but were confined within the circles of 
their own beliefs. Newton's discovery cast men's minds into an entirely 
new mould, and levelled many barriers to human progress. This intel- 
lectual result was vastly more important than the practical advantages 
of the discovery. It is true that navigation and commei'ce mightily 
benefited by oui- better knowledge of the motions of the heavenly bodies. 
Still, these benefits to humanity are incomparably less in the history of 
progress than the expansion of the human intellect which followed the 
withdrawal of the cramps that confined it. Truth was now able to 
discard authority, and marched forward without hindrance. Before this 
point was reached Brnno had been burned, Gralileo had abjured, and both 
Copernicus and Descartes had kept back their writings for fear of offend- 
ing the Church. 

The recent acceptance of evolution in biology has had a like effect in 
producing a far profounder intellectual change in human thought than 
any mere impulse of industrial development. Already its application to 
sociology and education is recognised, but that is of less import to human 
progress than the broadening of our views of Nature. 

Abstract discovery in science is then the true foundation upon which 
the superstructure of modern civilisation is built ; and the man who 
would take part in it should study science, and, if he can, advance it for 
its own sake and not for its applications. Ignorance may walk in the path 
lighted by advancing knowledge, but she is unable to follow when science 
passes her; for, like the foolish virgin, she has no oil in her lamp. 

An established truth in science is like the constitution of an atom in 
matter — something so fixed in the order of things that it has become 
independent of further dangers in the struggle for existence. The sum 
of such truths forms the intellectual ti-easure which descends to each 
generation in hereditary succession. Though the discoverer of a new 
truth is a benefactor to humanity, he can give little to futurity in com- 
parison with the wealth of knowledge which he inherited from the past. 
We, in our generation, should appreciate and use our great possessions — 

For me j-our tributary stores combine, 
Creation's heir ; the world, the world is mine. 



EEPOETS 



ox THE 



STATE OF SCIENCE. 



EEPORTS 



ON THE 



STATE OF SCIENCE. 



Report of the Committee, consisting of Professor G. Carey Foster, 
Sir W. Thomson, Professor Ayrtox, Professor J. Perry, Pro- 
fessor W. Gr. Adams, Lord Kayleigh, Dr. 0, J. Lodge, Dr. John 
HoPKiNSON, Dr, A. ]Muirhead, ]Mr. W. H. Preece, Mr. H. Taylor, 
Professor Everett, Professor Schuster, Dr. J. A. Fleming, Pro- 
fessor Gr. F. Fitzgerald, ]Mr. R. T. Gla/ebrook {Secretary), Pro- 
fessor Chrystal, ]Mr. H. Tomlixson, and Professor W. Garnett, 
appointed for the pmrpose of constructing and issuing practical 
Standards for use in Electrical Measurements. 

The Committee report tliat during the year the standards of resistance, 
ia terms of the legal ohm referred to in the last Report, have been con- 
structed, and their values determined ia accordance with the resolution 
adopted on June 25, 1884. 

The one-ohm standards were generally referred to the original B.A. 
units of the Association by combining in multiple arc with the standard 
one of the 100 B.A. units, and determining by Carey Foster's method the 
difference between the combination and a B.A. unit, and then assuming', 
in accordance with the resolution, that 1 B.A. unit ^ '9889 legal ohm. 

The following values were thus found for the two standards. 

The temperatures were taken by a thermometer graduated to tenths 
of a degree centigrade, which had been compared with the Kew standards. 





Resistance Coil, Elliott, No. 139, ^ 100. 




Date 


Temperature 


Resistance 


Nov. 24, 1884 
,. 26, „ 
,, 27, „ 
.. 28, „ 

Dec. 5, „ 
12 

July 30,' 188.5 
,. 28, „ 








ll°-4 
11°-G 
12°-9 
13°-5 
13°-5 
15°3 

n°-2 

18°^l 


•99878 
•99890 
•99916 
•99930 
•99931 
•99979 
1^00027 
1-OOOGl 



Mean value . 
Temperature cosfEcient 



■999515, at 14°^1 C. 
•000271 



32 



EEPORT — 1885. 



Resistance Coil, Elliott, No. 140, ^ 101. 



Date 


Temperature 


Resistance 


Nov. 24, 1884 . 


ll°-4 


•99813 


,. 25, „ 








ll°-5 


-99815 


Dec. 2, „ 








12°-8 


•99847 


Nov. 27, „ 








12°-9 


•99851 


Dec. 5, „ 








18°-4 


•99865 


„ 12, „ 








15°-4 


•99917 


July .30, 1885 








17°-2 


-99961 


„ 29. „ 








18=-0 


•99983 



Mean value . 
Temperature coefficient 



•998815, at 14°-1 C. 
•000259 



The ten-olim standards were tlien compared with the one-ohm by 
means of the arrangement suggested by Lord Rayleigh, and described in 
the Report for 1883, and from these values were obtained for tlie coils of 
higher resistance. 

The results are contained below. 



No. of Coil 


Resistance 


Temperature 


No. 141, ;^ No. 102 


10-00103 


lG°-7 


No. 142, ;^ No. 103 


10-00169 


16°-75 


No. 143, ;^No. 104 


99-9977 


16°-05 


No. 144, "^ No. 105 


100-0108 


16°05 


No. 145, "^ No. 106 


1,000-306 


17°-4 


No. 146, ;^ No. 107 


1,000-276 


17°-4 


No. 147, ^ No. 108 


10,002-4 


17°-35 


No. 148, ^ No. 109 


10,002-4 


17°-35 



These experiments were carried out at the Cavendish Laboratory by 
the Secretary and Mr. H. Wilsou, of St. John's College. 

At the request of M. Mascart, the Secretary compared with the 
legal ohms of the Association three mercury copies of a legal ohm, 
constructed by M. J. R. Benolt, of Paris. A detailed account of these 
experiments was laid before the Physical Society.' The values found are 
given below. 



No. of Tubes 


Value found bv 
M. J. R. Bcnoit 


Value found bv 
K. T. G. 


Diff 


37 
38 
39 


1-00045 

1-00066 

•99954 


-99990 

1-00011 

-99917 


•00055 
■00055 
■00037 


Moan 


1-00022 


•99972 


•00049 



' ridl. Mil//. Oct. 1885. 



ON STANDARDS FOR USE IN ELECTRICAL MEASURE5i'ENTS. 



33 



The work of testing resistance-coils has been continued, and a table 
of the values found for the various coils examined is given. 

British Association Units. 



No. of Coil 


Eesistance in B.A. Units 


Temperature 


Elliott, No. 122 f 
$^ No. 61 1 
Elliott, No. 58 


10-0163 

100017 

9-9885 

9-9834 


19°-8 
15°-2 
10' -5 
14°05 



Legal Ohms. 



No. of Coil 


Jlesistance in Legal Ohms 


Temperature 


"^ No. 150 
^ No. 151 
Elliott, 149, '^ No. 152 
Elliott, 136, '^ No. 153 

:^ No. 154 


•99895 
•99974 
•99912 
•99977 
100032 


ll°-7 
13°-9 
12°-5 
12°-4 
17°-3 



The Committee hope that arrangements may be made for issuing 
standards of electro-motive force and constructing standards of capacit3\ 
In conclusion, they would ask to be reappointed, with the addition of the 
names of Professor J. J. Thomson and Mr. W. N. Shaw, with the re- 
newal of the unexpended grant of 60/. 



Report of the Committee, consisting of Professors A. Johnson 
(Secretary), J. Gr. MacGtREGOR, J. B. Cherriman, H. T. Bovey, 
and Mr. C. Carpmael, appointed for the purpose of promoting 
Tidal Observations in Canada. 

The Committee have represented to the Canadian Government the 
importance of publishing tide-tables for Canadian waters, and the neces- 
sity for this purpose of establishing stations for continuous tidal observa- 
tions, recommending that the observations be subsequently reduced by 
the methods of the British Association. 

They have pointed to the example of the United States Government, 
which has provided tide-tables for both the Atlantic and Pacific coasts. 

In urging the practical side of the question they have more especially 
referred to the tide-tables for British and Irish ports published by the 
Admiralty, which give the rate and set of the tidal currents in the waters 
surrounding the British islands ; and they have drawn attention to the 
heavy annual losses caused by ignorance of these currents in Canadian 
waters, as shown by the wreck list. 

1885. D 



34 EEPORT — 1885. 

In ordei' to strengthen their representation from this point of view, 
they deemed it well to get the opinions of Boards of Trade and ship- 
owners and shipmasters. On inquiry it appeared that the Montreal 
Board of Trade were at the very time considering the qnestion, which 
had been brought independently before them. On learning the object of 
the Committee they gave it their most hearty support, and addressed a 
strong memorial on the subject to the Dominion Government. 

The Boards of Trade of the other chief ports of the Dominion also 
sent similar memorials. The shipowners and masters of ships, to whom 
application was made, were practically nnanimons in their testimony as 
to the pressing need for knowledge on the subject. 

The representations of your Committee were made through the 
Minister of Marine, with whom an interview was obtained, at which a 
memorial was submitted. Copies of the answers of the shipmasters (a 
large number of which had been received) were submitted at the same 
time. Full explanations, in reply to the inquiries of the Minister, were 
given, more especially on practical points connected with the proposed 
observations at fixed stations and the reductions, for which your Com- 
mittee are largely indebted to a corresponding committee appointed by 
the Council, consisting of the Right Hon. Sir Lyon Playfair, Professor J. 
Couch Adams, Sir William Thomson, and Professor Darwin. 

During the session of Parliament the Royal Society of Canada also 
addressed petitions to the Governor-General and the two Houses of 
Parliament, strongly urging the need of tidal observations. 

The reply of the Minister of Marine stated that, owing to the large 
outlay on the Georgian Bay Survey, and on the expedition to Hudson's 
Bay during the past summer (18S5), the Government did not propose to 
take action in the matter of tidal observations at present. This un- 
favourable answer, it will be observed, is made to depend on a temporary 
financial condition, and your Committee have reason to believe that if 
the financial ]irospects improve by next session of Pai-liament, the Govern- 
ment will take the matter into earnest consideration ; they therefore 
suggest that the Committee be reappointed. 



Fifth Report of the Committee, consisting of j\Ir. John jNIurray 
(Secretary), Professor Schuster, Professor Sir William Thomsox, 
Professor Sir H. E. KoscoE, Professor A. S. Herschel, Captain 
W. DE W. Abxey, Professor Bonney, Mr. E. H. Scott, and Dr. J. 
H. Gladstone, appointed for the purpose of investigating the 
practicability of collecting and identifying Meteoric Dust, and 
of considering the question of undertaking regular observations 
in various localities. 

The Secretary reported that collecting apparatus had been sent to various 
oceanic islands, and that a report would be prepared by next year on the 
specimens received. 



ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 35 



Third Report of the Gommittee, connsting of Professors G. H. 
Darwin and J. C. Adams, for the Harmonic Analysis of Tidal 
Observations. Drawn up by Professor G. H. Darwin. 

I. Record of Work during the past Year. 

The edition of the compntafcion forms referred to in the second report is 
now completed, and copies ai'e on sale with the Cambridge Scientific 
Instrument Company, St. Tibbs' Row, Cambridge, at the price of 2s. GtZ. 
each. Some copies of the first report, in which the theory and use of 
those forms are explained, are also on sale at the same price. A few 
copies of the computation forms have been sent to the librarians of some 
of the principal Scientific Academies of Europe and America.* 

In South Africa, Mr. Gill, at the Cape, and Mr. Neison, at Natal, are 
now engaged in reducing observations with forms supplied from this 
edition. 

A memorial has been addressed to the Government of the Dominion of 
Canada, urging the desirability of systematic tidal observation, and the 
publication of tide-tables for the Canadian coasts. There seems to be 
good hope that a number of tide-gauges will shortly be set up on the 
Atlantic and Pacific coasts, and in the Gulf of the St. Lawrence. The 
observations will probably be reduced according to the methods of the 
British Association, and the predictions made with the instrument of the 
Indian Government. 

Major Baird has completed the reduction of all the tidal results obtained 
at the Indian stations to the standard form proposed in the Report of 1883, 
and Mr. Roberts has similarly reduced a few results read before the 
Association by Sir William Thomson and Captain Evans in 1878. All 
these are now being published in the ' Proceedings of the Royal Society,' 
in a jmper by Major Baird and myself. 

A large number of tidal results have been obtained by the United States 
Coast Survey, and reduced under the superintendence of Professor Ferrel. 
Although the method pursued by him has been slightly different from that 
of the British Association, it appears that the American results should be 
comparable with those at the Indian and European ports. Professor 
Ferrel has given an assurance that this is the case ; nevertheless, there 
appears to be strong internal evidence that, at some of the ports, some 
of the phases should be altered by 180°. The doubt thus raised will 
probably be removed, and the paper before the Royal Society will 
afford a table of reference for all — or nearly all — the results of the 
harmonic method up to the date of its publication. 

The manual of tidal observation promised by Major Baird is now com- 
pleted, and will be published shortly. This work will explain fully all 
the practical difficulties likely to be encountered in the choice of a station 
for a tide-gauge, and in the erection and working of the instrument. 
Major Baird's great experience in India, and the success with which the 
operations of which he has had charge have been carried out, render his 

' Namely, the Koyal Societies of London and Edinburgh, the Royal Irish Aca- 
demy, the Academies of Paris, Berlin, and Vienna, the United Coast Survey, and the 
Cambridge Philosophical Society. 

D2 



36 REPOKT — 1885. 

advice of great value for tlie prosecution of tidal observation in other 
conntries. The work also explains the method of measuring the tide 
diaorams, entering the figures in the computation forms, and the sub- 
sequent numerical operations. 

II. Certain Factors and Angles used in the Reduction of Tidal 

Observations. 

In completing the reduction of the results of harmonic analysis to the 
standard form, a number of angles and factors are required which de- 
pend on the longitude of the moon's node. Tables of these angles and 
factors have been computed under the superintendence of Major Baird.' 
It may happen, however, that the tables are inaccessible to the computer, 
and the computation from the full formulae might be somewhat laborious. 
It happens that the angles r, £, v', 2v" (the meanings of which are ex- 
plained in the Report of 1883) are all expressible in the form 
A sin iV+B sin 2iV+C sin 3i^+ , 

where N is the longitude of the moon's node, and that the coefiBcients 
diminish with such rapidity that the first two terms are probably sufficient 
for all practical purposes. 

Also the several factors f are reducible to the form 

A + B cos N+G cos 2^+ . . . . , 

and three terms are practically sufficient. 

I have obtained the approximate formulze given below in this form. 
The rigorous results having been tabulated, it appeared easier to work 
from them instead of from analytical expressions in terms of the longitude 
o£ the moon's node. I find, then, the following results : — 

Schedule I. Approximate Formula; for Angles. 
.' =12°-9 sin A^-l°-3 sin 2N, 
I =,'-l°-07 sin N, 
(forK,) v' =z8°-8sinN-0°-6sm2N, 
(for Ka) 2»'"=17°-8 sin N- 0°-5 sin 2^^, 
Also A =16°-51 + 3°-44 cos ^-0°-19 cos 2N, and A,=16°-36. 
For the meanings of A and A^ the reader must refer to Part IV. 

Approximate Formulce for Factors f. 
For Mj and other tides, 

f = — cos^ U ^1-0003 _ -0373 cos iV-l--0002 cos 2N. 
cos'' ^o) cos* -^i 

For 0, f= . ^'" -^,^"^' ^^^ , =1-0088 + 1886 cos J^--0146 cos 2A^. 
sm w cos'^ io) cos* ^i 

ForK2 f= 1-0243 + -2847 cos A'+ -0080 cos 2Jv^. 

ForKi f=l-0060 + -1156 cos Jv^- -0088 cos 2iVr. 

ForMf . . f= . /'''' ^, , =1-0429 + -4135 cos .^-•0040 cos 2^. 
sm'' <i> cos* ^4 

• Some of these are given in the Report of 1883. 



ON THE HARMONIC ANALTSIS OF TIDAL OBSERVATIONS. 37 

For Mm, 

(1— Isin^w) (1— fsin^i) 



f= ^7~K^]f \ ■ ., .. =l-0000--r299 cos N+ -0013 cos 2N. 



Even if all the terms in 2N were omitted, the approximations might be 
good enough for all practical purjioses. 



III. On the Periods chosen for Harmonic Analysis in the 
Computation Forms. 

Before proceeding to the subject of this section, it may be remarked 
that it is unfortunate that the days of the year in the computation forms 
should have been numbered from unity upwards, instead of from zero, as 
in the case of the hours. It would have been preferable that the first 
entry should have been numbered Day 0, Hour 0, instead of Day 1, 
Hour 0. This may be rectified with advantage if ever a new issue of the 
forms is required, but the existing notation is adhered to in this section. 

The computation form for each tide consists of pages for entry of the 
hourly tide-heights, in which the entries are grouped according to rules 
appropriate to that tide. The forms terminate with a broken number of 
hours. This, as we shall now show, is erroneous, although this error may 
not be of much practical importance. 

In § 9 of the Report for 1883 the following passage occurs : — 

' The elimination of the effects of the other tides may be improved by 
choosing the period for analysis not exactly equal to one year. For 
suppose that the expression for the height of water is 

Ai cos ?!i< + Bi sin jii^ + Ao cos 7i2i-fB2 sin «2^ • • • (^1) 

* where 11.2 is nearly equal to «i, and that we wish to eliminate the 
n2-tide, so as to be left only with the «i-tide. 
' Now, tbis expression is equal to 

{A,+A2Coa (?ii— ?i2)«^ — Bo sin («i — «-2)^} cos n^t) 
+ [Bi+A2 sin (71,— «2)i + B2 COS ('h— 7J2)0 sin «ii] * 

' That is to say, we may regard the tide as oscillating with a speed tiy, 
but with slowly varying range.' 

Although this is thus far correct, yet the subsequent justification of 
the plan according to which the computation forms have been compiled 
is wrong. 

In the column appertaining to any hour in the form we have n^t a 
multiple of 15°, if n^ be a diurnal, and of 30°, if 71^ be a semidiurnal 
tide. 

Consider the column headed 'phours ' ; then nit=15° p for diurnals, 
and 30°_p for semidiurnals. 

Hence (62), quoted above, shows us that, for diurnal tides, the sum of 
all the entries (of which suppose there ai'e 2) in the column numbered 
y-hours, is 



38 EEPORT — 1885. 

cos lb°p{A^q + AJcoa(',H-n.^^ + co3[(in,-7io)(^^^ + ^J] 

+ cos[0h-«2)('2^ + i^')]+ . . ."]+P,[&c.]}+sml5°p{&c.} (a) 

And for semidiurnal tides the arguments of all the cii-cnlar functions in 
(a) are to be doubled. 

Now, we want to choose such a number of terms that the series by 
which A2 and Bo are multiplied may vanish. This is the case if the series 
is exactly re-entrant, and is nearly the case if nearly re-entrant. 

The condition is exactly satisfied for diurnal tides, if 

{ni—7i2)q — =27rr, 

where r is either a positive or negative integer. And for semidiurnal 
tides, if 

(?i, — ^2)2 — =27n'. 

That is to say, 

(^^ni—n2)q—nir, for diurnal tides, 
or 

(h, — H2)2=5'^i'*> for semidiurnal tides. 

It is not worth while attempting to eliminate the effect of the semi- 
diurnal tides on the diurnal tides, and vice versa, because we cannot be 
more than a fraction of a day out, and on account of the incommensurability 
of the speeds we cannot help being wrong to that amount. 

S Series. 

Now suppose we are analysing for the Sj tide, and wish to minimise 
the effect of the M2 tide. 

Then n,=2(y— »?)=2 xl5° per hour, 

712 = 2(7-0-), 

9;i-?!2=2(<r-'?)=l°0]58958 per hour. 

The equation is 

l°-01589582=15°r. 

If r=25, 2=369-13. 

Thus 25 periods of 2((7 — ??) is 369-13 mean solar days. It follows, 
therefore, that we must sum the series over 369 days in order to be as 
near right as possible. 

Now this is equally true of all the columns, and each should have 369 
entries. 

Hence, in order to have 369 entries in each column, the present 83 
computation form should have the last three entries cut off. The divisors 
are to be, of course, changed accordingly. 

M Series. 

Now consider that we are analysing for Mg, and wish to minimise the 
effect of the S., tide. Hence 



ON THE HARMONIC ANALYSIS OF TIDAL OBSEEYATIONS. 39 

n,=2(7 -,t)=2 X 14°-4920521 per hour, 

n2 = 2(y-r,), 

«,-,i2=_l°-0158958 per Lour. 
Hence, taking r negative, the equation is 

l°-01589582=14°-4920521r. 
If 5-25, 2=356-63. 

Thus 25 periods of 2(r7 — rj) is 356'63 of mean lunar time. 

It follows, therefore, that we must have 857 entries in each column. 

Thus the M, computation forni should have the row numbered 357 
complete, adding 9 more entries. 

There are no ' changes ' amongst these 9 entries. The divisors are 
to be modified accordingly, here and in all subsequent cases. 

K Series. 

To minimise the effect of Mg on K,, we have 

ni = 2y=2 xl5°-041068G per hour, 

«2 = 2(y-0, 

ni-«2=2(T-,,) = l°-0158958 per hour. 

l°-0158958g=15°-0410C86r. 

If r=25, 2=37014. 

Hence we should complete the row numbered 370. 

The last 3 entries of the existing tables are to be cut off. 

To minimise the effect of O on K,, we have 

w, = y=15°-0410686 per hour, 
112=7 -2<r, 
w,-H2=2<T=l°-0980330 per honr. 
l°-09803302=15°-0410686r. 
If r=27, 2=369-85. 

Thus 2=370 again gives the best result, and confirms the conclusion 
from the above. 

The N Series. 

Here 7ii=2y-3<7 + -ir=2 xl4°-2198648 per hour. 

To minimise the effect of M2, 

«2=2y — 2(r, 
ni— ??2=(<T-'57)=-0°-5443747 per hour, 
0-54437472=14°-2198648r. 
If r=13, 2=339-58. 

Hence we should complete the row numbered 340. 
There is no justification for the alternative offered in the computation 
forms of continuing the entries up to 369'' 3'^ of mean solar time. 

The L Series. 

Here ni = 2y-(T- ^=2 xl4°-7642394 per hour. 



40 REroKT — 1885. 

To minimise tlie effect of M2, 

)i,2^2y — 2(T, 
«j —n.2 = (T — '!!r=0°'5i4>S74i7 per hour. 
0'54437472=14°7642394r. 
If, .-=13, f^=352-58. 

Hence we should complete the row numbered 353. 
There is no justification for the alternative offered in the computa- 
tion forms of continuing the entries up to 369*^ 3*^ of mean solar time. 

The r Series. 

Hero 92,=27-3a-'sr + 2;j=2 xl4°-2562915 per hoar. 

To minimise the effect of M.,, 

^!2 = 27 — 2(7, 



n 



-i/2=-o--w+2>j=-0°-4715211 per hour. 



1 —"2 



0-471o211';=14-256291.5)-. 

Ifr=ll, 2=332-6, 

Hence we should complete the row numbered 333. 
There is no justification for the alternative offered in the computation 
forms of continuinp: the cnti ies up to 369'' 3^ of mean solar time. 

The X Series. 

Here ni=27-a + 'z^-2;/ = 2 xl4°7278127 per hour. 

To minimise the effect of Mj, 

n,=2y-2(T, 
«,,— 772=(T + «r — 2>;=0°-4715211 per hour. 
0-471521l2=14-7278127r. 
If r = ll, 2=343-58. 

Hence we should complete the row numbered 344. 
There is no justification for the alternative offered in the computation 
forms of continuing the entries up to 369*^ 3*^ of mean solar time. 

The 2N Series. 

Here w,=2y-4ff + 2'ar=2 xl3°-9476774 per hour. 

To minimise the effect of Mj, 

^2=27 — 2t, 
ni-n2=-2(o--'nT)=l°-0887494 per hour. 
l-08874942=13-9476774)-. 
Ifr=26, 2=333-08. 
Hence we must complete the row numbered 333. 

The T Series. 

Here 7ii=27-3»;=2 xl4°-9794657 per hour. 

To minimise the effect of M2, 

n^=2y-2rr, 
ni-«2=2T-3T = 0°-9748272 per hour. 
0-97482722=14-9794657r. 
Ifr=24, 3=368-79. 



ON THE HAiniONIC ANALYSIS OF TIDAL OBSERVATIONS. 41 

Hence we must complete the row numbered 369. 

The'R Series. 

Here wi=2y-»;=2 x 15°0205343 per hour. 

To minimise the effect of Mj, 

no=2r-2a, 
71, — «2=2ff — ii=l°"0569644 per hour. 
l-0569644(7=15-0205343)-. 
If r=25, 2=355-28, and r=2G, g=369-49. 

Hence we should either complete the row numbered 355 or that 
numbered 369. 

The 2MS Series. 

Here ni = 2y-4(T + 2»;=2 xl3°-9841042 per hour. 

To minimise the effect of M2, 

«2=2y-2^, 
M, -7i2= -2(<T-7;) = -1°-0158958 per hour. 
l'0158958r/=13-9841042r. 
If r=24, 2=330-37, and ?-=25, 2=044-13. 

Hence we should either complete the row numbered 330 or that 
numbered 344. 

The 2SM Series. 

Here Wi=2y + 2(r-4rj=2 xl5°-5079479 per hour. 

To minimise the effect of M,, 

«2=2y-2^, 
«,-n2=4(ff— r?)=2°-0317916 per hour. 
2-03179162=15-5079479)-. 
If r=48, 2=366-37. 

Hence we should complete the row numbered 366. 
The Series. 

Hero . n,=y-2(r=13°-9430356 per hour. 

To minimise the effect of Kj, 

ni-n2=-2ff=-l°-0980330 per hour. 
l-09803302=13-9430356>-. 
If r=27, 2=342-85. 

Hence we should complete the row numbered 343, cutting off the 
last three entries in the present forms. 

The P Series. 

Here «i=y-2,,=14°-9589314 per hour. 

It is open to question whether it is best to minimise the effect of 
K, or of O. 



42 EEroRT — 1885. 

For Ki take '>H=y, 

,ij-,i2=-2»j=-0°-0821372 per hour. 
0-0821372<7=14-9589314r. 
Ifr=2, 2=364-24. 

Hence we should complete the row numbered 364. 
For O, take ^2=7 — 2(t, 

,;.,_7i2=^2((T— 7j)=l°'0158958 per hour. 
l-01589582=14-9589314r. 
Ifr=25, 2=368-12. 

Hence we should complete the row numbered 368. 

It is better to abide by this, for in the former case n^ —n^ varies very 
slowly ; and we may be satisfied that on stopping with row 368 the effects 
of and Kj will both be adequately eliminated. 

The J Series. 

Here 7ii = y + (r— 'ct=15°-5854433 per hour. 

To minimise the effect of Kj, 

«2=r, 
Wj— n2='7 — 'nr=0°'5443747 per hour. 
0-5443747(7=15-5854433*-. 
If r=12, 2=343-56, and r=13, 2 = 37219. 

To minimise the effect of O, 

Wo=:y — 2(r, 
«j— n2=3(T-c7=l°-6424077 per hour. 
l-64240772=15-5854433r. 
If r=36, 2=341-6, and r=39, 2=370-09. 

Since in the latter case n^ — Ur^ varies three times as fast as in the 
former, it will be better to abide by this, and stop either with the row 
numbered 342 or that numbered 370. 

The Q Series. 

Here «i=y-3(r + '=7=13°-3986609 per hour. 

To minimise the effect of K,, 

?i2=y, 
,ii_,j2=-(3a-w) = -l°-6424077 per hour. 
l-64240772=13-3986609r. 
If r =38, 2 = 310-00. 

To minimise the effect of O, 

7i2=y — 2(T, 
n, — n2= — (ff — 'nr) = — 0°-5443747 per hour. 
0-54437472=13-3986609r. 
If r=12, 2=307-36. 
Since in the former case ni—V2 varies about three times as fast as in 



ON THE HAKMONIC ANALYSIS OF TIDAL OBSERVATIONS. 



43 



the latter, it will be better to abide by the former, and stop with the row 
numbered 310. 

With regard to the quaterdiurnal and terdiurnal tides, it does not 
signify where we stop ; but it seems more reasonable to stop with the 
exact year of 365 mean solar days. These tides are called MS, MN, 
MK, 2MK. 

Schedule II. 

Periods over which the Harmonic Analysis should extend. 



Initial of series 


Number of day and hour of 
last entry in special time 


Period elapsino; from O"* of spe- 
cial day 1 to 23'' of last special 
day in mean solar hours 


s 


369-1 23^ 


368'' 23h 


M 


357 23 


369 11 


K 


370 23 


368 23 


N 


340 23 


358 15 


L 


353 23 


358 14 


V 


333 23 


350 8 


X 


344 23 


350 8 


2N 


333 23 


358 2 


T 


369 23 


369 11 


E 


355 23 
or 370 23 


354 11 
or 369 11 


2MS 


330 23 
or 344 23 


353 22 
or 368 23 


2SM 


366 23 


353 23 





343 23 


368 23 


P 


368 23 


368 23 


J 


342 23 
or 370 23 


329 3 
or o56 1 


Q 


310 23 


347 



In the second column the numbers are given to the nearest mean 
solar hour. 



44 



EEroET — 1885. 



IV. A Comparison of the Haemonic Treatment of Tidal Observations 

WITH THE Older Methods. 

§ 1. On the Mefliod of Computing Tide-tables. 

There is nothing in the harmonic reduction of tidal observations 
which necessitates recourse to mechanical prediction of the tides. It 
may happen that it is desirable to produce a tide-table by arithmetical 
processes, and that the computers prefer to use the older methods of 
corrections, or it may be desired to obtain the tidal constants in the har- 
monic notation from older observations. For either of these purposes it 
is necessary to show how the liarmonically expressed results may be 
converted into the older form, so that the constants for the fortnightly 
inequality in time and height, and the corrections for parallax and 
declination, may be obtained from those of the harmonic analysis, and 
conversely. 

In the following sections I propose, therefore, first to reduce the har- 
monic presentment of the resultant tide into the synthetic form, where 
we have a single harmonic term depending on the local mean solar time 
of moon's transit, and on corrections depending on the R.A., declination, 
and parallax of the perturbing bodies. Subsequently it will be shown 
how a synthesis may bo carried out more simply by retaining the mean 
longitudes and elements of the orbits. 

§ 2. Notation for Mean Heights and llefardations derived from the Harmonic 

Method. 

The notation of the Report of 1883 is adopted ; and I shall carry the 
approximation to about the same degree as has been adopted by the older 
writers. Closer approximation ma}', of course, be easily obtained. 

In the Report of 1883 the mean height ' of a tide is denoted by H, 
and the retardation or lag by k. In the present note it will be necessary 
to refer to several of the H's and /.'s at the same time, and therefore it 
is expedient to introduce the following notation : — 

Schedule III. 



Initial of 


Mean height 


Retardation 


Initial of 


Mean height 


Retardation 


tide 


(H) 


(«) 


tide 


(H) 


i'^) 


Ma 


M 


2/x 


L 


L 


2\ 


S2 


S 


2i: 


T 


T 


2C 


Lunar K, 


K" 


2/v- 


R 


B 


24 


Solar K2 


K!' 


2/.- 





M' 


/-' 


K, 


K2 


2^- 


P 


S' 


<:' 


N 


N 


2r 

1 


K, 


^1 


'-"i 



In this schedule we assume T and R (of speeds 2y — 3ij and 27 — 77) to 
have the same lag as S2 ; and we use v in a new sense, the old )■, the 

' I use height to denote semi-range. All references to this Report will simply 
be by the date 1883. 




ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 45 

R.A. of the intersection of the equator with the lanar orbit, being 
denoted by r^. The initials of each tide are used to denote its height at 
any time. 

§ 3. Introduction of Sour-angles, Parallaxes, and Declinations. 

We must now get rid of the elements of the orbit and of the mean 
longitudes, and introduce hour-angles, declinations, and parallaxes. 

At the time t let a, ^, xp he 5 'sR.A., and declination, and hour-angle, 
and n^, ^'^, \p^, © 's R.A., and declination, and hour-angle. 

Let Z be 5 's longitude in her orbit measured from ' the intersection,' 
and a — I'o (I'o being the r of 1883) be D 's R.A. measured from the 
intersection. 

The annexed figure exhibits the relation of the several angles to one 
another. 

The spherical triangle affords the relations 

tan (fi — ro)^cos/tanZ, sin o=sin7sinZ .... (1) 

From the first of (1) we have, approximately, 

a = ?+r^-tan2iIsin2Z (-2) 

Now, s — s is the moon's mean longitude measured from J, and s—p is 
the mean anomaly. Hence, approximately, 

Z = s— ^-|-2e sin(s— ;)) (3) 

And therefore, approximately, 

a = s + »'o — s + 2esin(s— J)) — tan^^/sin 2(s— ^) . . . (J.) 
Now, t-\-li being the sidereal hour-angle, 

4. = <-|-7i-a (5) 

Therefore, from (4) and (5), 

f + /i_s-(r„-£)=i//-f2esin(s-p)-tan2iZ"sin2(s-£). . (6) 
By the second of (1) we have, approximately, 

cos2c = l — |sin-l4-Jsin2/cos2(s— I) .... (7) 

Hence, if A be such a declination that cos-A is the mean value of cos^ o, 
we have 

cos^A =1— isin^ J ) 

(8) 



^2a, 



and cos^A^= 1 — ^sin^ 

From this we have (neglecting terms in sin'* A) the following relations: — 
cos^ ^1= cos^A, sinlcos^ il= V2sinAcosA, sin^ J= 2sin2 A, 
cos'* -1^ = cos'- A ^, sinwcos^^w^ -%/2sina) cos w, sin-w=2sin2 A^. 



46 



REPOET 1885. 



Thus we may put 
cos* il 



cos^ A 



sin2A\ 



sin Jcos^ jl 
sin (o cos^ ^ w CDS'* it sin 2 A^ 



tanHI=itan2A 



cos* ^a> COS* ^i COS- A, 

sin^I _sin2A 

sin2w(l — o-sin^t) sin'^A/ 
An approximate formula for A and the ralue of A, are 

A = 16°-51 + 3°-44cosN-0°-19 cos 2N, A =16°-36 

The introduction of A and A^ in place of I and w entails a loss of 
accuracy, and it is only here made because former writers have followed 
that plan. It may easily be dispensed with. 

Now let us write 



(?) 



(10) 



D=cos2(s— i), 
n=cos(s— p), 

From (7) and (8), 

J. cos^ c — cos^ A 

sm^ A 



D'=sin2(s-£)' 
n'=sin (s— p) 



J-, sine cos? do 

ffsin^A dt 



(11) 



(12) 



Then, if we write for the ratio of the moon's parallax to her mean paral- 
lax P, we have 

P — 1 = ccos(s— j>), 



and 



n'=- 



dP 



(13) 



n = -(P-l), - , . n 

e e{rT — ij) at 

Hence D, D', IT, IT are functions of declinations and parallaxes. The 
similar symbols with subscript accents are to apply to the sun. 
Now (G) may be written by aid of (9) and (11), 

o[; + 7,_5_(,,^_t)]=2J/ + 4en'-D'tan2A . . . (14) 

The left-hand side of (14) is the argument of M, (see Sched. B. i. 
1883), and from (9) the factor of M., is cos^A/cos^A,. Hence, subtracting 
the retardation 2ju from (14) we have 

(Mo)=-^^3/cos[(2-^H-4en'-D'tan2A)-2/x], 
' cos-A; 

expanding approximately, 

(Mo)=^-^4^3fcos2(>i.-A.) 
cos^'A^ 



cos-A 
cos"^A, 
sin^A 
cos^A, 



n'43fesin2(4/-/i) 

D'3Isin2(J.-^) (ir.) 



We shall see later that the two latter terms of (15) are nearly 

annulled by terms arising from other tides, and as in the case of the sun 

the rates of change of parallax and declination are small, we may write 

by symmetry, 

^ (So) = Scos2(v/.,-0 (IG) 



ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 47 

In all the smaller tides we may write 

A general formula of transformation will be required below. Thus, if 
cos2a'^X, sin2.ii=X', 

:^ -sin2(;/.-^) . (17) 

C0S2(ct — yti) y-r r/ V y 

The lunar Kn tide. 

From Sched. B. i., 1883, we have 

Lunar K2=^,-^'°!^Ji:"cos2r^ + 7i-ro-'^-] 
sin-(.i(l— l^sin-^t) o J 

''"^Z"cos2[v;/+(s-0-'^-]- 



sm 



Applying (17) with X=D, X'=D', a=/.-, and taking the lower sign, 

In the case of the sun we neglect the terms in D', for the same reasons 
as were assigned for the similar neglect in (16), and have 

Solar Ko=7r/'Z),cos2(4.,-/.) (19) 

The tide N. 

From Schedule B. i.. Report 1883, 

COS'^WCOS'^l ^ V z-/ J 

^^'^ (N)=^^^cos2[;^-,.-K«-p)]. 

Then applying (17) with X=U, X'=n', a = r, and taking the upper 
sign, bat writing ^t — r instead of j' — ^(, because this tide being slower 
than M2 suffers less retardation, 

(N)=^5^^r(n+tan2(^-r)n')cos2(;//-r) 

The tide L. 

We shall here omit the small tide of speed 2y — ff + 'nr, by which the 
true elliptic tide is perturbed. Thus the B in the column of arguments 
in Sched. B. i., 1883, is neglected, and we have 



48 KEPOKT — 1885. 

Applying (17) with X=n, X'=n', n=\, and taking the lower sign, 
and changing the Bign of the whole, because of the initial negative sign, 



(L) = ^^^^Lr(-n-tan2(\-//)n')cos2(v/.-X) 

COS^-!k/ L 

n2(+-rtj . (21) 

4 



I 



cos2(\— y^t) 

The sum o/N and L. 

In order to fuse these terms an approximation will be adopted. The 
L tide is just as much faster than Mo as N is slower, but the N tideshould 
be nearly 7 times as great as the L tide; hence the tan2(\-/t) in (21) 
will be put equal to tan2(^-)0. We then have 

(N) + (L)=-^r(n + tan2(/.-On')(^cos2(»/.-,')-Lcos2(;/.-\)) J 
COS -^/L " 

+ n'(A"sec2(/x-.) + Lsec2(\-^))sin2(^-^.)]- 

J^cos2rJ/->0— Lcos2(>/.-X)=cos2;/.(A^cos2)'-Lcos2\) 

+ sin 2ijt'(W'sin 2i-isin2X). 

Then writing 

, o iV'sin2i' — Lsin2\ /^qx 

JVcos2>'— -Lcos2a 
BO that £ is nearly equal to r, we have 

^ ^^^ ■' cos^A^ cos2£ L J 

+ £!^r(i^sec2(^<-.')+i>8ec2(\-/z))sin2(>^-^)] . (23) 
cos-'AX J 

In the symmetrical term for the sun, with approximation as in (16), j 

^^^^^ (T) + (R)=(r-ii;)n,cos2(;//-0 (24) 

This terminates the semidiurnal tides which we are considering; but | 
before proceeding to collect the results some further transformations must 

be exhibited. -r^, , • n -n /i tx 

Let us consider the function D + xB', where x is small. From (12) 

we see that n • ^ 5 js 

cns'c— cos'^A 1 2 sine cos cad 

^ sin^A (T sin-'A at 

Hence, if S' be the moon's declination at a time earlier than the time of 
observation by x/2cr, then 

^_^^^,^cosV-cos^_ . 

sm'^A 

Hence, in (17), 

■n . ^ or ^n' cos^o'— cos^A .^.. 

D-ftan2(K — w)!* = r-:7\ .... (.^0; 

' sm^A 

when h' is the moon's declination at time tV^-57°-3 tan 2(k-^)/2(7. The 
period 57°-3 tan2((c-;:x)/2<7 may be called ' the age of the declinational 
inequality.' 



ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 49 

Again, 

e [ a — 'cjdt) 

Hence, if {F — Vjje denotes the valae of (P— l)/e at a time xj(ff — 'sr) 
earlier than that of observation, then 

n+an'=l(P'-i). 

e 
Hence, in (23), 

n + tan2(^-r)n'=l(P'-l) (26) 

where P' is the ratio of the moon's parallax to her mean parallax at a 
time tV'-'57°-3 tan 2(^-r)/(<7-^). The period 57°-3tan2(/x-r)/(<7-w) 
may be called ' the age of the parallactic inequality.' 
In collecting results we shall write the sum 

M2 + So + K2 + N + L + R + T = ;i2. 

For reasons explained below we omit terms depending on the rate 
of change of solar parallax and declination. 

Then, from (15), (16), (18), (19), (23), (24),' (25), (26), we have 

h, = ^^ M cos 2(4^ -fi) + S cos 2(4^-0 
cos-A^ 

sin^A, ^' ^ sm^A, ' ^^' * 

_sjnacosS cl2r K^ _af tan^A,") sin2(;^-^) 

ffsin^A^ f/^Vcos 2(ic— /x) / 



, COS^A.T,, T .^COS 2^ — ^003 2/\ r>/ 1 \ 

+ — 2^(P'-1) 5 cos2(4/-£) 

cos^'A, ecoszt 

+ (P^-l)i?!:iZ^cos 2(;/.,-0 



cos- A_ 1 dP f^ ^j._ Nsec2(ft-v) + Lsec2(\-fx) 
COS- A, (T — tn- dt 



r41f-^^'^^«^(^-") + ^^""^(^-^)^sin2(^-;,) 

(27) 

It may easily be shown, from Schedule B. i., 1883, that in the eqni- 
librium theory 'it" — If tan2A,=0, and 4M—(N+L)/e=0; hence the 
terms depending on rates of change of declination and parallax are small. 
This also shows that we were justified in neglecting the corresponding 
terms in the case of the sun. Also, since the faster tides are more 
augmented by kinetic action than the slow ones, the two functions, 
written above, which vanish in the equilibrium theory are normally 
actually positive. The formula (27) gives the complete expression for 
the semidiurnal tide in terms of hour-angles, declinations, and parallaxes, 
with the constants of the harmonic analysis. 

We shall now show that with rougher approximation (27) is reducible 
to a much, simpler form. 

The retardation of each tide should be approximately a constant, plus 
1885, E 



50 REroRT — 1885. 

a term varying -n'ith the speed. Hence all the retardations may be 
expressed in terms of ^ and /x, and 

K =[1+ (T, 



'hiT-^), 



a — 1] 

(T — 7/- 

It Is clear that i: differs very little from 4, and that 

^-At_ 2(M- »)_4-/t 
a a — •Z3- a — i) 

The time (^—M-)K<^—v) is called 'the age of the tide,' for reasons 
explained below, and K — fj, fi — r, not being large angles, do not differ 
much from these tangents. Hence the ages of the declinational and 
parallactic inequalities are both approximately equal to the age of the 
tide. 

Let ce, then, denote (if— /i)/((T— ?/), the age of the tide. 

Now, as an approximation, we may suppose that heights of the lunar 
K2 tide, the N and L tides bear the same ratio to the Mo tide as in the 
equilibrium theory ; and that the solar Ko, the T and R tides bear the 
same ratio to the S2 tide as in that theory. Then reverting to the nota- 
tion with J, w, i in place of A, A„ and writing 

\ cos iw cos ^1 J 
we have 

sin^A T-'/ -pSin^ J^,, cos^A ,- r^fir cos- A 



-K!'=-^^'\UM, ^""^.^N = leBT, "^^L=iefJ/; 



sin^ A , cos'' -gl cos- A , " cos- A ^ 

COS''^u> 

Also, since (22) may be written 

tan(2u_20=-^'''"--^'--^t:5^2(X-^ 

we have, treating fi — >•, X— /^, /' — « as small, approximately, 

£=;ii-|(;e(ff-'=7)=;t-|(\-r). 

Also 

cos^A iVcos 2i' — L cos 2X _ „,, 

— 2"- 7, -=.3eflf. 

cos^ A , cos Ze 

Then reverting to mean longitudes, and substituting the age of tide 
where required, we find, on neglecting the difference between k and i', 

For the lunar declinational term, 

2 tan2Ufi/cos2[s-a;<T-4'] cos 2(^|y-i;)', 

For the solar declinational term, 

2 tan2 iw S cos 27i cos 2(^p,-0 ; 

For the lunar parallactic term, 

3eflf cos [s— p — cpfff — ot)] cos 2[;^— yn + ^a'((T — •ar)] ; 



ON THE HAEMOMIC ANALYSIS OF TIDAL OBSEKVATIONS. 51 

For the solar parallactic term, 

3e,(S' cos (h—pi) cos 2[i!'/ — 4]. 

Then omitting the terms depending on changes of declination and 
parallax, we have as an approximation, 

7i2=filf fcos 2(>^-^) + 2 tan^iJcos 2[s— a'o— £] cos 2(v/'-0 

+ 3ecos [s— ^ — f[;(<T — ffl-)] cos 2[-.//— yL( + |((,'((T — -ct)] 

+ ,S [ 1 +2 tan- hw cos 2h + 3e, cos (h-p,) 1 cos 2(4/,- 4) . . (28) 

In the equilibrium theory we have the lunar semidiurnal tide depend- 
ing on r~3 cos- c cos 2i//. Now it is obvious that cos^ introduces a 
factor 1 + 2 tan- ^Icos 2 (s — ^), and i"^ a factor 1 + 3e cos (s—p). Thus, 
if we could have foreseen the exact disturbance introduced by friction and 
other causes in the various angles, the formula (28) might have been 
established at once ; but it seems to have been necessary to have recourse 
to the complete development ia order to find how the age of the tide will 
enter. 

§ 4. Reference to Time of Moon's Transit. 

It has been usual to refer the tide to the time of moon's transit, and 
we shall now proceed to the transformations necessary to do so. 

cos- A /cos^ A, goes through its oscillation about the value unity in 
19 years ; it is therefore convenient to write for, say, a whole year, 

c^A_3^ ~ 



(29) 



cos-' A / 

and similarly, N^z=^^'A N 
cos^ A ; 

7- cos^ A 
COS'' A J 

"We also observe that K" and Kf, being the lunar and solar parts of 
the mean K., tide, and their ratio being -464 (Report, 1883), 

K" = -68303K„ K/'=-3l697K^ .... (30) 

It will also be seen that in all the terms arising from the sun, exceptincr 
that in K/', the argument of the cosine is 2(\P,-i;). It will be con°- 
venient, and sufficiently accurate for all practical purposes, to replace 
ichy 'C in this solar declinational term Jv'/'. 

We shall now proceed to refer the tide to the moon's transit at the 
place of observation. 

Let a„, h^ be D 's R.A and 's mean longitude at ]) 's transit— say 
upper transit, for distinctness. Then the local time of transit is given by 
the vamshing of I, and since xl^=t-\-h-a, it follows that the time-angle 
ot D s transit (at 15° to the hour) is ci^ — h^. 

Now let T (mean solar hours) be the interval after transit to which the 
time-angle t refers ; then, since 

E2 



52 REroKT — 1885. 

=[(y-'j)^ + «o-/'o] + [/'o + 'r]-['.o + Tr+('~-TV], 

For the sake of brevity-, put 

T = (y-<7)T, 

so that T is r converted to angle at the rate of 14°'49 per hour. Then 
we have 

v/.=T-(^;^-.)r (31) 

Similarly putting o^ for 's R. A. at D 's transit, we have 






SO that 

(la 



Then let 

^=«o-a, (32)* 

So that A is the apparent time of ]) 's transit, reduced to angle at 15° 
per hour, and we have 

;/.,=T + -l+('r-J^)r (33) 

It is only in the two principal tides that we need regard the changes 
of R.A. since B 's transit, and in all the smaller terms we may simply put 

The first pair of terms of (28) now become 

iLr„cos2[T-(^^-ay-^] + .S'cos2[T + 4+(^^-^p)r-4], 
and these are equal to 

lf„ cos 2(T -/.) + ,S cos 2(T 4- ^ - 

"We may now collect together all the results, and write them in the 
form of a schedule. 



* It would be better to put 
If this bo used the correction (iO) for Q's change of R.A. becomes small. 



4 (T — ri 

•y — a 



ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 



53 







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54 REPOET— 1885. 

Definition of symbols : — 

a, 5, a„ d, D 's and 's R.A. and declination at moon's transit ; 

A=a — Uj, apparent time of 1) 's transit at the port. 

57°'3 
I' 3) 'sdecl.atthetime(generallyearliertliantransit)r ~ — tan2((v — /i). 

JitT 

F, P/ the ratio of D 's and 0's parallax to mean paralla,xes. 
P' the ratio for )) at the time (generally earlier than transit) 
7— tan2(/u — )'). 

r the time elapsed since ]) 's transit in m.s. hours ; T the same time 
reduced to angle at 14°'49 per hour. 

A such a declination that cos^ A is the mean value of cos^ o ; A has a 
lO-yearly pei'iod. 

A^ such a declination that cos^ A, is the mean value of cos- c,. 

e, e, eccentricities of lunar and solar orbits ; a the D 's mean motion ; 
«7 the mean motion of the }) 's perigee. 

^^^o^io^COS^ A 

M IS L cos^A; 

M, S, K<i, N, L, T, B the mean semi-ranges II of the tide.? of those 
denominations in the harmonic method. The retardations found by 
harmonic analysis are 2^i for M,, 2i^ for S.), 2/c for K.>, 2i' for N", 2\ for L, 
and 2^ for T and R. ' " " . 

Lastly tan 2e= — ^^ ^ — j ^ 2^ ^q be taken in the same quadrant 

'' iVcos2)'-ivcos2\ • '■ 

as 2,'. 

§ 5. Synthesis of the Several Terms. 
Consider the two principal terms in Schedule IV. 

M, cos 2(T - ^0 + ,S' cos 2 (T + ^ - . 

They may be -wi-itten in the form 

fl'cos2(T-^), 
where H cos2(n — (j,)=M^ + S cos 2(J. — i+/j), 

Hsin2(i^-,l>) = Ssm2(A-^ + fi). 

If we compute f corresponding to the time of moon's transit fi'om the 
formula 

tan2(^-^)^ .Ssin2M-^ + ^) 



'M, + Scos2(A-(+fiy 

then (f> reduced to time at the rate of 14°-49 per hour is the interval 
after moon's transit to liigh water, to a first approximation. The 
angle + 90°, similarly reduced, gives the low waters before and after the 
high water, and (j!>-j-180° gives another high water. The high waters 
and low waters are to be referred to the nearest transit of the moon. 
The height or depression is given to a first approximation by 

jff=^/(j\J„2 + g2 + 2iTf„S cos 2 (/x-.^)). 



OS THE HAKJIONIC ANALYSIS OF TIDAL OBSERVATIONS. 55 

This Tariabilitv in the time and height of high water, due to variability 
of (,'>, is called the fortnightly or semi-menstrual inequality in the height 
and interval. The period (:^ — /.i) j (cr — i]) is called ' the age of the tide,' 
because this is the mean period after new and full moon before the 
occurrence of spring tide. 

§ 6. Corrections. 

The smaller terms in Schedule IV. may be regarded as inequalities in 
the principal terms. They are of several types. Consider a term 
£cos2(T-/3). 

Then 

i?cos2CT-/3)=5cos2(/3-0)cos2(T— 0)+5sin2O3-0)sin2(T-0). 

Hence the addition of such a term to ffco8 2(T — ^) gives us 
(H+dE) cos 2(T-f-l<p), where 

cH=B cos 2(ft-(p),2m(p=Bsm2(i3-(l.). . . . (35) 

Next consider a term C sin 2(T — /^t). Putting /5=yLi + l-, we have 

'cR=-Csin2(^i-<p),2Eo<i>=Gcos2(^-(p) . . . (36) 

Xext consider a term E cos 2(T4 .4 — i^). Putting /3=^—A, we have 

cE=Ecos2(A-i:+<l>),2Hcf=-Esin2(A-i:+<i,) . . (37) 

Lastly, consider a term JPsin 2(T + J. — 4). Putting /3=^— J. + |7r, we 
Lave 

cE=Fsm2(A-!:+<l>),2El(p=Fcos2(A-C + (p) . . (38) 

In writing down the corrections we substitute 14'49S^ for c(j), and 
introduce a factor so that the times may be given in mean solar hours and 
the angular velocities in degrees per hour. 

Change of Moon's R.A., Sched. IV. 
This is of type (36), and gives 



This correction to the height is very small. 

Cliancje of Sun's R.A., Sched. IV.* 
This is of type (38), and gives 



(89) 



(40) 



* "With the value of A suggested in footnote to (.32) {a - da, j dt)r becomes 
[((p-/i)tr-(<p^a, jdi-nv)] I iy — <r) at high water. This is obviously very small. 



56 



REPORT — 1885. 



Moon's Declination, Sclied. IV. 
This is of type (35), and gives 



oif=^^5^i^^^^-683Ji2Cos2(^— .ji) 



sin'' A/ 
.^^-^^.gj,j,cos^a^-cos2_A 
sin^ Aj 

Sun's Declination, Sclied. IV. 
This is of type (37), and gives 



•6835 sin 2 (».— </.) 



(41) 



cH=^^^lIlZ^2!l^ -317 K2Cos2(A-( + <)>) ' 

3f = -lh-977^5^!A:i^£?!^' -.317 ^ sin 2(A-i: + (p) 
sin''' A, M 



(42) 



Change of Moon's Declination, Sched. IV. 
This is of type (36), and gives 

SH='^^^l^ da 7 -683 K, Mts^n^A,) sin 2(;.-^)) 

ffsm^^, dt\cos2{t:-fi) 'J ^^ [(4.3 

sin ? cos 2 cU f •683/1, ^ ' 



U= - P-977- 



(tH sin^ A 
Moon's Parallax, Sched. IV. 
This is of type (35), and gives 



, dt \co92{k-ii) 7 ^^ ^') 



cB={p'^iy^ 



N„ cos 2t' — L. cos 2\ 



e cos 2£ 



cos 2(£ — 0) 



t<=lh-977(P^-l)^'° "°" ^'-^° ^"" '^^ sin 2(£-<^) 

i/e cos 2£ 

Sun's Parallax, Sched. IV. 
This is of type (37), and gives 

afl"=(P,-l)^^ cos2(4-4+f)' 

ct= -lh-977(P,-I)^^ sin 2(^-C + «/') 

Change of Moon's Parallax, Sched. IV. 
This is of type (36), and gives 



(44) 



(45) 



m=^^ ^f414- ^°^"^^<^-") + ^°^""^^^-^) Uin2(u-ri,)l 

1--977 dP^^^^^_ N^sec2(^-r) + L^.ec2(X-,) ^ ' 

{a—'m)H dt\ e J J 



H= 



(46) 



The lunar corrections involving sines are small compared with those 
involving cosines. 

To evaluate these corrections -we must compute r from f reduced to 
time at 14°'49 per hour. 

In the right ascenaionalterms, da/dt and a are to be expressed in 
degrees per hour, da/dt is the hourly change of ))'s H.A. at time of 
B 's transit, and dajdt is the hourly change of © 's R.A. at time of D 'b 
transit. 



ON TUE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 57 

Similarly, dcjdt is to be expressed in degrees, if a be in degrees. 
c', P' can be found for the antecedent moments, 57'''3 tan 2(k- — ^()/2o-, 
and 57°'3 tan 2(/i — i')/(t — ■or), before the time t. 

§ 7. The Diurnal Tides. 

I shall not consider these tides so completely as the semidiurnal ones, 
although the method indicated would serve for an accurate discussion, if 
it be desired to make one. 

The important diurnal tides are Ki, 0, P. 

From Schedule B ii., 1883, we have 

sinlcosHI M'cos [f + 7.-,.,-2(.-0 + iU-//]. 
sm w cos-' ^w cos'' ^^ 

By (9) the coefficient is sin 2^ /sin 2^„ and we shall put, as in the 
case of the semidiurnal tides, 

bin ZA^ 
Then, since t + h-=-^ + a, 

(0)=J/o' cos [4'+(a + ''o)-2(s-0+i'^-A''] 

=MJ cos ii, for brevity {'^7) 

Again, from Schedule C, 1883, 

(P) = ,S'' cos [i-Zi + K-;"] ; 
Then let x=2(s-/0 + 'o-2^-4' + m'> and we have 

(?) = «' cos (il + x) (48) 

Whence 

(0) + (P) = [lfo' + <S' cos xl cos a-S' sin x sin fi. 

If we pnt, 

E' cos {i^'-<i>')=MJ + S' cos X 

H'sin (^'-.^')='S'Binx. 

(0) + (P)=fi' cos (O + m'-^') 

=ir'cos[>/. + («->0-2(s-^)+i7r-f] . (49) 



Where 



R'=s/ {ilA'2 + 6"2 + IM^S' cos xl 

and tan (a'-d,')= ^l^^'^J^ — 

'^^ ' ^ 34' + /S"cosx 



(50) 



The rate of increase of the angle x is twice the difierence of the mean 
motions of the moon and sun, but it would be more correct to substitute 
for s and li the true longitudes of the bodies. It follows from (50) that 
^' has a fortnightly inequality like that of <l>. 

\p is very nearly equal to T, and where the diurnal tide is not very large 
we may with sufficient approximation put 

(a-rj-2(s-0=-(s-,0. 
So that with fair approximation 

(0) + (P)=fl'cos[T-(s-0 + |7r-^'] . . . (51) 



58 iiErouT — 1885. 

The synthesis of the two parts of the Kj tide has been performed in 
the harmonic method (Report, 1883), and we have 

(K,) = fi7iri cos (t + h—y' — hTr — i:^). 

Then, writing iJ{i=K„, we have 

(K,)=7v„ cos (T + a-.''-i7r-/.i) .... (5-2) 

We have next to consider what corrections to the time and height of 
high and low water are necessary on account of these diurnal tides. 
If we have a function 

A=I7 + B'cos2(T-./)) + B"iCOs(«T-/3), 

where n is nearly equal to unity, and H^ is small compared with H; its 
maxima and minima are determined by 

sin 2(T-f/>)= -^- sin (nT -/3). 

If T=To be the approximate time of maximum, and To + oTq the true 
time, then, since the mean lunar dayis24"84 hours, and the quotient when 
this is divided by Stt is 0'^'988, we have in mean solar hours, 

oT,= -0-988^^-sin(7iT,-/3) "i 

And the correction to the maximum is 

■ ^cH=E, cos (nT,-l3) 

Again if T=Ti be the approximate time of minimum, and Tj + cT, 
the true time, then 



(53) 



cTi ^0-988^ sin (7iTi-/5) 



(54) 



And the correction to the minimum is 

m=Hi cos (nTy- ft) 

In the case of the correction due to (0) + (P))''' is approximately 

1 , and for the correction due to Ki, n is approximately l-\ 

y — <T y — a. 

§8. Direct Synthesis of the Harmonic Expression for the Tide. 

The scope of the preceding investigation is the establishment of the 
nature of the connection between the older treatment of tidal observa- 
tion and the harmonic method. It appears, however, that if the results 
of harmonic analysis are to be applied to the numerical computation of a 
tide-table, then a direct synthesis of the harmonic form may be preferable 
to a transformation to moon's transit, declinations, and parallaxes. 

Semidiurnal Tides. 

"We shall now suppose that M^ is the height of the M^ tide, augmented 
or diminished by the factor for the particular year of observation, accord- 
ing to the longitude of the moon's node, and similarly K^ generically for 
the augmented or diminished height of any of the smaller tides. As 



ON THE IIARMOXIC ANALYSIS OF TIDAL OBSEKYATIONS. 09 

before, let 2/j, 2^' bo the lags of Mo, So ; and 2v, generically, the lag of 
the K tide. 

Let 6=l + h-s-y^ + E. 

Then 6 might be defined as the mean moon's hour-angle, the mean 
moon coinciding with tlie true, not at Aries, but at the intersection. 
Let the argument of the K tide be written genericallj' 2\_0 + u~i:']. 

Then 

h,=M„eos2(6-fi) + Scos2[8 + s-li + v^-^-!:]+K,cos2[0 + u-K'\ 

. . . (55) 
If we write 

So ^=4 ''o + s, 
and 

E cos 2 (ju - f) =M^ + S cos 2[s-Ji- ; „ + ^, ] 

Hsin 2(^L-f) = S sin 2[..--7i-4o + A']. 
the first two terms of (55) are united into 

Hcos2(e-fi>) (56) 

with fortnightly inequality of time and height defined by 
tan2(,-^)== S.in2(s-h-i:^ + ,)_^ 

E= v/ [ ir,2 + ,s2 + 2MS cos 2 (s - 7. - f „ + ^) ] ) 

The amount of the fortnightly inequality depends to a small extent 
on the longitude of the moon's node, since (^ 3"tl M^ are both functions 
of that longitude. 

For the K tide we have 

Ka cos 2(d + n — K)=K^ cos 2(u — K + (p) cos 2((i — </.) 

— Ko sin2(u — K + (p) sin 2(6 — (p). 
Hence 

2H"= K^ cos2(u — K+(j)) ] 

K .... (58) 

cf=-^sm2(u-. + ^) ) 

It is easy to find from the Nautical Almanac (see Moon's Libration) 
the exact time of mean moon's transit on any day, and then the successive 
additions of 12''-4206U1 or 12^ 25™ 14sl6 give the successive upper and 
lower transits. The successive values of 2(s — h) may be easily found by 
successively adding 12°-6180o6 to the initial value at the time of the first 
transit of the mean moon, and may be obtained from the table of the 
fortnightly inequality for each value of 2(.s— 7i). 

The function ti is slowly varying, e.g., for the K2 tide 2u=2(!i — t,) 
+ 2(i'o — )'"), and the increment of argument for each 12*'-420G01 may be 
easily computed once for all, and added to the initial value. 

In the case of the diurnal tides it will probably be most convenient to 
apply corrections for each independent]}-, following the same lines as those 
sketched oiit in § 5. 

The corrections for the over tides M4, S4, &c., and for the terdiurnal 



60 KEPOBT— 1885. 

and quaterdiarnal compound tides, would also require special treatment, 
which may easily be devised. 

At ports, where the diurnal tide is neai-ly as large or lai'ger than the 
semidiurnal, special methods will be necessary. 

Although the treatment in terms of mean longitudes makes the cor- 
rections larger than in the other method, yet it appears that the compu- 
tation of a tide-table may thus be made easier, with less reference to 
ephemerides, and with amply suflBcient accuracy. 



Report of the CoTnviittee, consisting of Mr. Robert H. Scott 
{Secretary), Mr. J. Norman Lockyer, Professor Gr. Gr. Stokes, 
Professor Balfour Stewart, and Mr. Cf. J. Symons, appointed 
for the purpose of co-operating with the Meteorological Society 
of the Mauritius in their propjosed publication of Daily 
Synoptic Charts of the Indian Ocean from, the year 1861. 
Dratvn up by Mr. E. H. Scott. 

The Committee have the honour to forward, for the inspection of tlie 
members of the Association, a cop}' of the Charts for the month of March 
1861, with some specimens for January of the same year, and the com- 
plete number for February which appeared some years ago. These docu- 
ments have recently arrived from the Mauritius. 

As the work has now made decided progress, the Committee have 
a])plied for and obtained the grant of 50^. placed at their disposal by the 
General Committee. 

As soon as the requisite documents are received from Dr. Meldrum, 
the Committee will submit a formal account of their expenditure with 
the necessary vouchers. 



Report of the Committee, consisting of Mr. James N. Shoolbred 
(Secretary) and Sir William TH0MS0^', appointed for the re- 
duction and tabidation of Tidal Observations in the English 
Channel, made ivith the Dover Tide-gauge ; and for connecting 
them tvith Observations onade on the French coast. 

Your Committee herewith beg to submit the High Water and the Low 
Water Observations for the years 1880, 1881, 1^82, and 1888, obtained 
from the records of the self-registering tide-gauges at the ports of Dover 
and of Ostend respectively. 

The observations, in order to facilitate comparisons, are reduced to 
Greenwich time and to the common datura-plane of 20 feet below the 
Ordnance datum of Great Britain. 

As the reduction and tabulation of the present series of tidal observa- 
tions has proved a longer operation than was anticipated, there has been 
hardly sufficient time to consider the best form in which those observa- 
tions should be placed for comparison, nor for the more suitable deductions 
which may be drawn from such comparison. 

Your Committee, therefore, request to be reappointed. 



ON STAXDABDS OF WniTE LIGHT. 61 



Report of the Comviittee, consisting of Professor Gr. Forbes (Secre- 
tary), Captain Abxey, Dr. J. Hopkixsox, Professor W. Gr. Adams, 
Professor Gr. C. Foster, Lord Rayleigh, Mr. Preece, Professor 
Schuster, Professor Dewar, Mr. A. Vernon Harcourt, and Pro- 
fessor Ayrton, appointed for the purpose of reporting on Stand- 
ards of White Light. Drawn up by Professor Gr. Forbes. 

The experimental work of tlie Committee during the past year has not 
been extensive, as they had no funds at their disposal for expei'imental 
research, and they have been chiefly occupied with reviewing what has 
been done in the past and laying plans for future operations. 

Lord Rayleigh has constructed an instrument which he calls a mono- 
chromatic telescope, by means of which the illuminated screens of a photo- 
meter may be examined, allowing light only of one definite colour to pass. 
It was hoped by Lord Rayleigh that experiment might show that, with 
some suitably chosen colour, this instrument, nsed with any ordinary 
photometer, would, in comparing lights of different intensities and tem- 
peratures, give to each a candle-power which would be sufficiently 
accurate to represent for commercial purposes the intensity of the light. 
The Secretary has made some experiments at the Society pi Arts, where 
he was kindly permitted to use the secondary batteries and glow lamps ; 
but the results so far are not definite enough to justify their publication. 

Mr. Vernon Harcourt has been engaged on an investigation on the 
barometrical correction to his pentane standard, and on another con- 
cerning the possibility of using lamp-shades as a protection from air 
currents. His researches are communicated independently to the meeting. 

Captain Abney and General Testing have continued their observations 
on the intensity of radiations of different wave-lengths from incandescent 
carbon and platinum filaments at different temperatures, which will go far 
to assist the Committee in their work. 

Other isolated experiments have been made by members of the Com- 
mittee, which will be published in due course. 

Most of the members have examined the experiments of the Trinity 
Board at the South Foreland. 

Existinrj Standards. 

A consideration of existing standards convinces the Committee that 
the standard candle, as defined by Act of Parliament, is not in any sense 
of the word a standard. The French ' bee Carcel ' is also liable to vari- 
ations ; and with regard to the molten platinum standard of Violle, it 
seems that the difficulty of applying it is so great as to render its general 
adoption almost impossible. 

With regard to the so-called standard candle, the spermaceti em- 
ployed is not a definite chemical substance, and is mixed with other 
materials, and the constitution of the wick is not suflSciently well defined. 
Hence it is notorious that interested parties may prepare candles con- 
forming to the definitions of the Act which shall favour either the pro- 
ducer or consumer to a serious extent. In view of these defects of the 
standard candle, it is a matter of great importance that a standard of 
light should be chosen which is more certain in its indications. 

The Committee have looked into the merits of different proposed 
standards, and the majority feel satisfied that, for all the present com- 



G2 REroRT— 1885. 

mercial requirements, the pentane standard of Mr. Yernoii Harcourt — 
since it lias no wick and consumes a material of definite chemical com- 
position — when properly defined, is an accurate and convenient standard, 
and gives more accurately than the so-called standard candle an illumi- 
nation equal to that which was intended when the Act was framed. 

Yet the Committee, while desiring to impress the Board of Trade and 
the public with these views, do not feel inclined at present to recommend 
the adoption of any standai'd for universal adoption until, further in- 
formation on radiation having been obtained from experiment, they may 
learn whether or not it may be possible to propose an absolute standard, 
founded, like electrical and other stpndavds, on fundamental units of 
measurement — a standard which, for these reasons, would be acceptable 
to all civilised nations. They are, howevei', inclined to look upon the 
pentane lamp as an accurate means of obtaining an illumination to replace 
the so-called standard candle. 

Froposed Experimental Hesearcltes. 

Radiation is measured as a rate of doing work, and consequently 
radiation might be measured in watts. The illumination (or luminous 
effect of radiation) depends partly upon the eye, and is a certain function 
of the total radiation. This function depends upon the wave-length of 
the radiation, or on the different wave-lengths of whicli the radiation, if 
it be compound, is composed. This function of the radiation perceived 
by the eye is partly subjective, and varies with radiations of different 
wave-lengths and with different eyes. Thus the illumination cannot, like 
the radiation, be expressed directly in ab.^olute measurement. But the 
connection between the illumination and the radiation can be determined 
from a large number of experiments with a large number of eyes, so as to 
get the value of the function for the normal liuman eye. This function, 
however, is constant only for one source of light, or, it may be, for sources 
of light of the same temperature. It appears, then, that, in the first 
instance at least, a standard should be defined as being made of a definite 
material at a s-pecial temperature. 

The energy required to produce a certain radiation in the case of a thin 
filament of carbon or platinum-iridium heated by the passage of an electric 
current can be easily measured by the ordinary electric methods, and the 
radiation may be measured by a thermopile or a bolometer, which itself 
can be standardised by measuring the radiation from a definite surface 
at 100° C, compared with the same at 0° C. The electric method 
measures the absorption of energy ; the thermopile measures the total 
radiation. These two are identical if no energy is wasted in convection 
within the glass bulb of the lamp, by reflection and absorption of the glass, 
and by conduction ffom the terminals of the filament. Captain Abney and 
General Festing have come to the conclusion that there is no sensible loss 
from these causes. The Committee propose to investigate this further. 
This constitutes a first research. 

No research is necessary to prove that vvith a constant temperatui'e of 
a given filament the luminosity is proportional to the radiation, because 
each of these depends only upon the amount of surface of the radiating 
filament. It will be necessary, however, to examine whether with 
different filaments it be possible to maintain them at such temperatures as 
shall make the illumination of each proportional to the radiation. This 
will be the case if spectrum curve^', giving the intensity of radiation in 



ON STANDAKDS OF WHITE LIGHT. 63 

terms of tl\c wa%-e-lengtli when made oiTfc for tbe different sources of light, 
are of the same form. Thus a second research must be undertaken to 
discover whether the infinite number of spectrum radiation curves, which 
can be obtained from a carbon filament by varying the current, are 
identical in form wiion the filament is changed, but the material remains 
so far as possible of constant composition. 

It will be an object for a later research to determine whether, when 
the radiation spectrum curve of any source of light has been mapped, a 
similar curve can be found among the infinite number of curves which 
can be obtained from a single filament. 

The next stc]) proposed is to e.\amine a large number of carbon or of 
platinum-iridinm filaments, and to find whether the radiation spectrum 
curve of different specimens of the same material is identical when the 
resistance is changed in all to x times the resistance at 0° C. If this 
law be true, a measurement of the resistance of the filament would be a 
convenient statement of the nature of the radiation curve. If, then, a 
number of filaments were thus tested to give the same radiation spectrum 
curve, their luminosities would in all cases be proportional to their 
radiations, or (if there be no loss in convection, conduction, absorption, 
and reflection) proportional to the electrical energies consumed. 

Thus it might be hoped to establish a standard of white light, and to 
dctlneit somewhat in the following manner: — ^4 zinit of light is ohtained 
from a straigJit carbon fila'inent, in the direction at right angles to the middle 
of the filament, when the resistance of the filament is one-half of its resistance 
at 0° C, and when it consumeslO^ C.G.S. units of electrical energyper second. 

Since Mr. Swan has taught ns how to make carbon filaments of 
constant section by passing the material of which they are composed 
throuo-h a die, it is conceivable that another absolute standard should be 
possible — viz., a carbon filament of circular section, with a surface, say, 
TiTij ^l- centimetre, and consuming, say, 10^ C.G.S. units of energy per 
second. 

Whether such standards are possible or not depends npon the experi- 
ments of the Committee. The probability of success is suflBcient to render 
these experiments desirable. 

Proposed Later Experimental Researches. 

Should these hopes be realised, and an absolute standard of white 
light thus obtained of a character which would commend it to the civilised 
world, it would then become an object of the Committee to find the ratio 
of luminosity when the radiation spectrum curve of the standard filament 
is varied by varying the current, and consequently the resistance of the 
filament. 

Thus, by a large number of subjective experiments on human eyes, a 
multiplier would be found to express the illumination from the standard 
lamp, with each degree of resistance of the filament. 

A reseai'ch, previou.sly hinted at, would then be undertaken — viz., to 
find whether the radiation spectrum curves of all sources of illumination 
agree with one or other of the curves of the standard filament. It is not 
improbable that this should be the case except for the high temperature 
of the electric arc. 

Should this be found to be true, then photometry would be very 
accurate, and the process would be as follows: — Adjust the standard fila- 
ment until its radiation spectrum curve is similar to that of the lijht to he 



64 REPORT — 1885. 

compared. (This would probably be best done by obsei'ving tlie wave- 
length, of the maximum radiation, or by observing equal altitudes on 
either side of the maximum, the instruments used being a spectroscope 
and a line thermopile or a bolometer.) The total radiation of each is then 
measured at equal distances by the thermopile. The resistance of the 
filament is measured, and its intensity in terms of the unit of white light 
obtained therefi-om by the previous research. The luminosity of the 
compared source of light is then obtained directly. 

The Committee desire to be reappointed, and to enable them to carry 
out the researches indicated they ask for a grant of 30^. 



Second Report of the Committee, consisting of Professor Balfour 
Stewart (Secretary), JNIr. J. Knox Laughton, Mr. Gr. J. Symons, 
]Mr. R. H. Scott, and Mr. Johnstone Stoney, appointed for 
the purpose of co-opjerating luith Mr. E. J. Lowe in his pjroject 
of establishing a Meteorological Observatory near Chepstow on 
a permanent and scientific basis. 

Since theh- reappointment in 1884 this Committee have met twice, and 
have placed themselves in correspondence with Mr. Lowe. 

In this correspondence the Committee have expressed their opinion 
that the establishment of a permanently endowed meteorological observa- 
tory ou a good site, such as that of Shire Newton, is a matter of undeniable 
scientific importance. 

The attitude whicli the Committee have taken will be rendered appa- 
rent by the following letter written by their Secretary to Mr. Lowe : — 

' The Committee request me to point out to yoa that the main feature 
of your proposal, which interests the British Association and the scientific 
public generally, is the prospect which it holds out of the establishment 
o? a permanent institution by means of which meteorological constants 
could be determined, and any secular change which may take place 
therein in the course of a long period of years be ascertained. It will be 
for you and the local authorities to decide what amount of work of local 
interest should be contemplated, and on this will the scale of the observa- 
tory mainly depend. The Committee are therefore unable to say what 
amount of capital would be required. They would point out four con- 
ditions which they hold to be indispensable : — 

'1. The area of ground appropriated should be sufficient to ensure 
freedom from the effect of subsequent building in the neighbourhood. 

' 2. A sufficient endowment fund of at least 150L annually should be 
created. 

' 3. The control should be in the hands of a body which is in itself 
permanent as far as can be foreseen. 

' 4. The land for the site shall be handed over absolutely to the above- 
mentioned governing body.' 

This communication from the Committee is now under the considera- 
tion of Mr. Lowe and his friends, but until the precise amount of the 
local meteorological requirements is ascertained and further progress is 
made in the scheme the Committee consider that they would not be justi- 
fied in any more prominent action than that which they have already taken. 

They would request their reappointment, and that the unexpended sum 
of 2hl. be again placed at their disposal. 



ON COMPARING AND EEDUCING MAGNETIC OBSERYATIONS. 65 



Report of the Committee, consisting of Professor Balfour Stewart 
{Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick 
Evans, Professor Gr. H. Darwin, Professor Gr. Chrystal, Professor 
S. J. Perry, Mr. C. H. Carpmael, and Professor Schuster, 
appointed for the purpose of considering the best means of 
Com/paring and Reducing Magnetic Observations. Brawn up 
by Professor Balfour Stewart. 

In presenting their report to the Britisli Association the Committee 
would begin by referring to the appendix, in which are embodied sug- 
gestions of great value which they have received from men of science at 
home and abroad. The Committee desire to express their thanks to the 
authors of these contributions. 

While a final discussion of these communications cannot be attempted 
in this first report, it is nevertheless evident that magneticians are not 
agreed as to the best method of determining absolutely the solar-diurnal 
variations of the three magnetic elements — that is to say, the diurnal 
variation resulting after the elimination of all disturbed obsei'vations. 
The point in dispute is the method of distinguishing and separating the 
disturbed from the undisturbed observations. On the whole, the feeling 
is against the method of Sabine, on account of the arbitrary nature of his 
separating value. 

An alternative method has been proposed by Dr. Wild, Director of the 
Central Russian Observatory (Appendix, No. VII.). This method seems 
to be in some degree analogous to that pursued at Greenwich (Appendix, 
No. IX.). Dr. Wild selects those curves which appear to the eye to be 
free from the short-period irregularities characteristic of disturbances, 
and considers the results obtained from their measurement to embody a 
trustworthy representation of the solar- diiirnal variation for the time and 
place in question. He finds a remarkable uniformity and simplicity of 
type in the variation as given by the difi"erent selected curves. 

While the Committee recognise in this a method which may ultimately 
meet with general acceptance, they think there are various points con- 
nected with it which require investigation. 

In the first place, it would be desirable to prove, by means of an 
exhaustive discussion of some one element — as, for instance, the declina- 
tion — to what extent curves selected by the eye do, as a matter of fact, 
present this uniformity and simplicity of type. 

There are abundant materials available for this purpose at the Kew 
Observatory, and it is hoped that through the kindness of the Kew 
Committee this point may eventually be settled. 

Again, it would be desirable to ascertain whether the apparently 
normal days at one station coincide with those at another ; and, if so, 
whether there is a definite or nearly definite relation in type and range 
between the corresponding smooth curves of two widely separated stations 
of not very dissimilar latitude. 

This point will form one of the subjects of a discussion undertaken by 
Sir J. Henry Lefroy, who proposes to compare the curves of Toronto and 
those of Greenwich together for the years 1849-53. 

1885. F 



66 REPORT — 1885. 

The Committee are of opinion that these are steps \vhich might at 
once be taken, so as to push on this part of the subject. 

The Committee -would call attention to the completeness of the mag- 
netical information which is given by the present method of publication 
adopted by the Astronomer Royal. He now gives, in addition to the 
mean values of the magnetic elements for each day and the mean diurnal 
curves for each month, the amplitade of the diurnal curve for each day, 
and particulars of all disturbances, small as well as large. (See Appendix, 

No. IX.) 

Until a method is generally accepted for determining the normal solar- 
diurnal valuation, it seems prematui-e to raise any discussion on the best 
■way of estimating disturbances, since these cannot well be measured 
except from the basis of such a normal. 

The Committee would, however, allude to various investigations, 
chiefly connected with disturbance, which are being undertaken by some 
of its members. The thought seems generally to have occurred that dis- 
turbances may denote the method by which the earth rights itself with 
respect to the magnetic forces acting upon it (see Appendix, No. II., para- 
graphs 11 and 12), and this idea underlies the various researches about 
to be named.' 

The first of these is that already mentioned as having been taken up by 
Sir J. H. Lefroy, with the concurrence of the Astronomer Royal — namely, 
a comparison oi magnetic movements photographically recorded at 
Toronto and Greenwich in the years 1849-53. Stations so far asunder 
(3,100 miles), and on different continents, appear calculated to throw 
light on many questions which are not much advanced by compaiison of 
stations in geographical proximity. 

The following are i^ri ma facie conclusions which may require modifica- 
tion when the work has been gone through, but which already seem to 
have a bearing on the physical explanation of the phenomena : — 

a. A similar state of magnetic weather, so to speak, prevails generally 
at both stations, so that where numerous or extensive deviations from 
normal regularity occur at the one, there is generally something corre- 
sponding at the other. 

h. The correspondence very seldom amounts to similarity of movement 
or identity of time. 

c. The changes of declination at Toronto are more rapid than at 
Greenwich. This is especially observable about the time of the morning 
easterly extreme. Bold sweeping curves with a long time measure are 
much less common at Toronto than at Greenwich, and can seldom be 
identified. 

d. On the other hand, shocks of small angular amount breaking a 
uniform line are often capable of identification, and are simultaneous, 
or nearly so, at both stations. 

e. Although the declination was westerly at both stations, the move- 
ments of disturbance are very frequently, probably usually, in opposite 
directions at any given time — easterly at Greenwich, or decreasing the 
absolute declination, when they are westerly, or increasing it, at Toronto. 

/. The same days would generally be selected to form normal curves 
at both stations. 

> A similar idea seems to have occurred to Dr. Wild (see foot-note to his communi- 
cation, Appendix, No. VII.). 



ON COMPARING AND EEDUCING MAGNETIC OBSERVATIONS. 67 

g. Sliglit auroral displays in Canada generally produce a mai'ked effect 
at Toronto, but none at Greenwich. 

h. It is not easy to answer the question whether a state of disturbance 
succeeding one of calm begins or ends at the same time at both stations, 
neither beginning or ending being, in general, sufficiently definitely 
marked. 

i. It appears impossible to assign a value based on angular movement 
alone which will be a valid test, whether such movement is due to dis- 
turbing causes or not. 

j. Angular movements at Toronto appear to be larger than at Green- 
wich, the magnets being (in 1849-50) similar — namely, 2 feet in length. 

The second research is by the Rev. S. J. Perry and Professor Stewart, 
who, with the sanction of the Kew Committee, are engaged in a com- 
parison of the simultaneous disturbances of the declination at Stonyhurst 
and at Kew. Calhng the first S, and the second K, they have obtained 
the following preliminary results, which may, however, ultimately require 
some modification : — 

(1) S is always greater than K, or the ratio ^ is always greater than 

unity. 

• (2) This ratio appears to depend in some way on the duration of the 
disturbance. 

(3) But not, as far as can be seen at present, upon its magnitude. 

A third research is by Professor Stewart and Mr. W. Lant Carpenter, 
who are making a preliminary trial of four years of Kew declination dis- 
turbances (separated by Sabine's method), in order to ascertain whether 
the aggregate daily disturbance depends upon the relative position of the 
sun and moon, and also whether it is affected by meteorological storms. 
The following provisional result has been obtained from the years 1870-73 
in which the lunation is divided into 8 parts, (0) denoting new, and (4) 
full moon. 

Mean Daily Aggregate of Disturbance of Declination at Kew} 
(Unit xo^^'b of an inch, measured on the curve.) 



(0) 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


111 


114 


104 


95 


83 


94 


107 


101 



The Committee desire to draw the attention of magneticians to the 
urgent need of obtaining more accurate knowledge than we possess at 
present of the daily variation of the vertical force. No attempt to fix 
the cause of the daily variation can be made until the daily variation of 
each component of the magnetic force is known. 

In conclusion, the Committee desire their reappointment, with the 
addition to their number of Captain Creak and of Mr. G. M. Whipple, 
Director of the Kew Observatory, and they would request that the sum 
of 50Z. should be placed at their disposal, to be spent as they may think 
best on the researches mentioned in this report. 

' The late Professor J. Clerk Maxwell was, it is believed, the first to suggest that 
the lunar-diurnal variation of the earth's magnetism maybe caused by distortion, and 
Dr. Schuster has suggested that, if there is found to be a relation between magnetic 
disturbances and atmos]pheric storms, it may be of the same nature. 

f2 



68 REPORT — 1885. 

APPENDIX. 

Suggestions for the Committee on Magneticcd Reductions. 

I. By Professor Balfoue Stewakt, F.R.S. 

1. The following suggestions are founded on the methods proposed by 
several magneticians, including Sabine, Broun, Lefroy, Capello, and Buys 
Ballot. To Senhor Capello I am especially indebted for the trouble he 
has taken in explaining his views, with which these suggestions are 
almost identical. 

2. The measurements derived from self-recording magnetographs may 
be used for two purposes, the first being to ascertain the solar diurnal 
variation, by which name we designate that variation which is exhibited 
by comparatively undisturbed observations. The second of these pur- 
poses is to ascertain the laivs ivliich regulate Jisturhances. Now disturbances 
may act in two ways. First, they may exhibit a diurnal variation different 
from that of the undisturbed observations, which we may call the dis- 
hcrhance diurnal variation ; and, secondly, they may exalt or depress the ^ 
day's value of the particular element in question. 

As a matter of fact I believe they act in both these ways. It appearsi 
to me that it is of very great importance that these two effects of dis-l 
turbance should be exhibited and studied togertier, and yet not impro- 
perly mixed up with one another. 

3. Let me explain my meaning with reference to the method of Sabine,! 
■which I believe to be, in many respects, an excellent one. Sabine did 
very great deal in finding out and exhibiting the diurnal variations of the' 
disturbed and undisturbed observations, but he did not greatly study, 
along with these, the effect of disturbances in altering the daily mean 
values of an element, so that it was reserved for Broun to discover that 
there were changes in the daily values of the horizontal force which were 
practically simultaneous at the various stations of the globe. Let us fii-st 
of all consider the hourly values of declination, as this element presents 
fewest difficulties. 

Declination, 

4. Here, I imagine, the first thing is to determine the solar diurnal 
variation, or that presented by the comparatively undisturbed observations, 
and for this purpose I fail to see a better plan than that proposed by 
Sabine. This method may be described as follows : 

5. Suppose that we have hourly observations at a station, then, first 
of all, we should arrange these into monthly groups, each hour by itself. 
We should then reject, as disturbed observations, all those which differ 
by more than a certain amount from their respective normals of the same 
month and hour, the normals being the hourly means in each month after 
the exclusion of all the disturbed observations. For the purpose of 
ascertaining the true solar diurnal variation, it seems probable that a 
considerable choice might be allowed in selecting the separating value 
implied in the above process, one value serving, for tliis pii^rpose, probably 
as well as another a little above or below it. 

6. Perhaps under ordinary circumstances a value which will exclude 
as disturbed about one-twentieth of the whole body of observations will be 
found convenient. 

7. Let us now imagine that we have determined by this process 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 69 

the undisturbed normpJs for eacli hour, for each month. I agree -with 
Sir J. H. Lefroy in thinking that the best plan of investigating disturb, 
ances is, in the first place, to obtain the various departures of individual 
observations from their respective normals for that month and hour. It 
would be desirable to embody these departures in a fresh table, in which 
(except for those who are colour-blind) the negative departures might be 
given in red ink and the positive in black. 

8. In this table, at the right of the twenty-four departures for the 
various hours of the day, I should represent the mean departure for that 
whole day either in red or black. It would thus be seen, at a glance, 
whether the average of the whole day was affected by disturbance, in 
what direction, and to what extent. 

9. It is here assumed that, during the month in question, no alteration 
of scale value or other instrumental change has taken place. Never- 
theless at stations which have a considerable secular variation of decli- 
nation, and for which this is known, it might be desirable to introduce, 
say to the extreme right, a column embracing a small residual correction, 
applicable to each day's departures, on account of secular change. 

10. I imagine that a monthly table, constructed after the method 
which I have described, will afford a full and satisfactory basis for the 
discussion of disturbances. 

11. It is probable that the smaller departures will follow the law of 
the ordinary solar diarnal variation, and, in that case, there should be as 
many Ijlach as red sums in these minor departures, or, in other words, the 
algeiaraic sum of these should be zero, while the sum taken without 
respect to sign or colour should represent the amount of oscillation or 
disturbance obeying the ordinary law, this being a point which it is of 
interest to determine. No doubt the larger disturbances will obey some 
other law, and it will be necessary to separate them into two categories, 
those increasing and those diminishing the declination. Here I should 
follow Dr. Buys Ballot's advice, and allow the observations themselves to 
determine where the one law ends and the other begins. It is just possible 
that sometimes the day's mean may be decidedly different fi'om what it 
ought to be, and yet the diurnal variation for that day be as nearly as 
possible the same as for undisturbed observations. A table, such as that 
now described, will show, at a glance, whether such a state of things ever 
takes place. 

Horizontal and Vertical Force. 

12. The horizontal and vertical force magnetographs are different 
from the declination magnetograph, inasmuch as their indications are 
affected by change of temperature, by loss of magnetism, and possibly, 
in the case of the vertical force instrument, by other circumstances not 
well understood. 

13. It will be noticed that, in treating the declination results by 
Sabine's method, we perform oar operation upon the individual declina- 
tion values. Now it might be said, why not (your object being to find 
the solar diurnal variation) take the dej^arture of the individual hours of 
a day from the mean of that day, and treat each month's departures by 
Sabine's method ? 

14. The reply would be that the mean of a day is more likely to be 
affected by disturbance than the monthly mean of an hour. For disturb- 
ances, when they come, generally affect several consecutive hours, thus 



70 REPORT — 1885. 

altering the daily mean, but, on the other hand, they are less likely to 
affect the same hour during consecutive days. Were we able to obtain 
daily means of declination, unaffected by disturbance, it would be better 
to adopt this method of treatment, because it would obviate the intro- 
duction of any residual correction due to the progress of secular change 
or annual or semi-annual variation. Now in the force magnetographs 
the case is different. Here there is a certainty that some — perhaps even 
a considerable — change will be produced in the values belonging to a given 
hour in the course of a month from instrumental changes alone, so that 
treating the observations after the manner pursued with the declination 
might lead to erroneous results. 

15. On the other hand, if there were no disturbance, the difference of 
the various hourly observations of a day, from the mean of that day, 
would give us a good indication of the solar diurnal vai-iation, provided 
the diurnal range of temperature was inconsiderable, as is generally the 
case for self-recording instruments. 

16. These remarks render it manifest that some method of obtaining- 
probable values of the undisturbed daily means is, in the case of the 
force instruments, of vital importance, and Senhor Capello has adopted 
a method of this kind in his treatment of his force observations. I would 
venture to remark that the most unexceptionable basis upon which to 
determine the undisturbed daily means of horizontal and vertical force 
would seem to be given by the information already assumed to be obtained 
from the declination magnetograph for the same month. 

17. Here, as a result of the application of Sabine's method, we have 
rejected a certain number of hourly observations as disturbed. Now let 
us reject, as a preliminary step to something more complete, precisely the 
same hourly observations of the horizontal and vertical force as being, in 
all probability, disturbed, and make use of the remainder, or of that part 
of the remainder which represents whole, or nearly whole, days free from 
disturbance, to aid us in determining, by a curve, the most probable values 
of the undisturbed daily means. I here assume that there is no sudden 
jump in the month's readings from change made on the instrument or 
any other cause ; if there be such, the portions before and after the jump 
will have different values, and must be treated by appropriate methods 
which need not here be discussed. Suffice it to say that, by rejecting 
from the month's observations those hours which were separated as dis- 
turbed in the declination, and treating the remainder in the manner 
suggested, we obtain, aided, perhaps, by a slight equalisation, numbers 
representing very nearly the undisturbed daily values of the records 
given by the insti'uments. 

18. Having obtained these, our next operation is to obtain the hourly 
differences from each day's undisturbed mean. These differences, so 
obtained, we i^ropose to treat in the same manner in which we treated 
actual declination observations. It is, therefore, to these differences that 
Sabine's process should be applied, so that ultimately, when we have 
applied it, we shall obtain those departures of each hour from the daily 
mean which characterise undisturbed observations — in other words, we 
obtain the solar diurnal variation. 

19. Having obtained this, we have at once the means of obtaining a 
table similar, in all respects, to that which we have recommended for the 
declination. For instance, if the departtire of a given hour of a given 
day from the undisturbed mean of that day were + 9 whereas, according 



ON COMPAEING AND KEDUCINa MAGNETIC OBSERVATIONS. 71 

to the solar diurnal variation for undisturbed observations, it should have 
been +3, the number +6 would be inserted in the table, and so on. 

20. It will be seen at once that we shall be able to ascertain by the 
method now described, if disturbance (as Broun supposed) alters the 
daily average values of the horizontal force. For in the horizontal force 
instrument any comparatively short period change of average daily value 
is hardly likely to be caused by instrumental alteration, but is most pro- 
bably due to magnetic causes, more especially if the same change take? 
place simultaneously at various stations. 

There are, however, moi-e serious difficulties connected with the 
vertical force instrument, but into these I cannot now enter. 

II. By Sir J. Hexet Lefeot, K.C.M.G., F.R.S. 

1. The statement of the question appears to assume that the first, or 
chief, object of continuous automatic registers of magnetic changes is to 
extend the large number we already possess of mean determinations of 
solar-diurnal variations, and to add fresh numerical or quantitative values 
of the deviations from these means, produced by the causes we class as 
irregular. 

2 . This appears to me to be persevering in a path we have been travel- 
ling for forty years Avithout reaching, or even seeing the way, to any 
physical explanation of the phenomena. 

3. There are about seventy-five points on the globe at which the 
diurnal variation, including disturbances, has been determined by eye- 
observations, hourly or bi-hourly, with more or less completeness and 
precision. The irregular, or non-solar-diurnal, effects have as yet been 
eliminated for a few only (ten or twelve) of these points, but this number 
has proved sufficient to bring out pretty clearly certain general laws to 
which no key has yet been found. 

4. Unless it can be shown, that a multiplication of numerical data 
promises to bring us to a conclusion, I am inclined to think that the 
laborious compilation of more data of the same kind by measurements 
from photographic registers, which are less precise than the old eye- 
observations, is rather a misdirection of energy, unless indeed at stations 
widely remote from any others, and where new facts may be expected 
(see, for example, the very anomalous diurnal curve at Reikiavik, Iceland, 
'Athabasca volume,' p. 297). The recent circumpolar stations would 
have come into this category if they had used self-recording instruments. 

5. Airy and Sabine have both taken ± 3'"3 of declination as the 
measure of a disturbed observation at Greenwich and Kew respectively.' 
If it is true, as remarked by Professor Balfour Stewart (par. 5), that the 
precise measure is of no great consequence, is it worth while to spend 
much time over making out a new value independently for any part of 
Great Britain ? 

6. The arbitrary nature of Sabine's mode of treatment of observations 
is to me a strong objection to the continuance of it. 

For example, he threw out as disturbed all the observations at Point 
Barrow which deviated 22'-87 from the normal,^ and at Fort Carlton ^ all 
which deviated 6'-0. But I think I have sufficiently shown that in high 
latitudes in America the mean value of disturbance is about three times 

' Phil. Trans. 1860-1863. - Phil. Trans. 1S57. ^ St. Helena, vol. ii. 



72 EEPOET 1880, 

as great in the early morning hours as it is in the afternoon. Conse- 
quently we must either disregard a great many observations by day, which 
are really disturbed, or include a great many by night, which are not, 
unless we say that instability is the same thing as disturbance. 

7. What, then, is to be done with the photographic registers ? How 
can they be compared unless by ordinates, measured at points agreed 
upon, such as the Gottingen hours ? 

I reply (1) that I think that each observer should minutely scan his own 
records, and note the time, direction, and amount of movements. (2) That 
the efiPorts of magneticians should be addressed to the cheap pulolication 
and prompt interchange of the registers of each week, reproduced and 
reduced by photography to a uniform scale, say 15mm. to 1 hour, with a 
view to the discovery of periodically recurring movements of whatever 
nature ; of movements apparently local, or not generally traceable ; and 
of movements which were general, in one or more elements, over a large 
part of the earth's surface. 

It hardly meets this suggestion to say that we have hundreds of 
projections of disturbances already, and that nothing has come of it. It 
is true ; but these projections are scattered through many volumes, are 
upon all sorts of scales, and are rarely comparative. 

8. The student having by his eye- comparison grasped the general 
features of the movements constituting disturbance at some particular 
epoch, or presenting an exceptional character, the need of measurements 
would arise, and if a reference to the mean of the day or the mean of n 
days or of the calendar month is necessary, such mean can be ascertained. 
I am not sure that it often will be, and I doubt whether our adherence to 
the calendar month is rational. Why should movements on May 31 be 
referred to the mean for May rather than the mean for June ? The more 
accurate, though more laborious, plan would be to refer them to the mean 
for May 31 ± 10 days. 

9. The end of the needle which points to the equatorial region has in 
every locality a mean position in relation to the meridian from which it 
is continually deviating, and to which it always returns. It appears to 
me open to question whether the relation of the direction of the move- 
ment to the absolute declination, as increasing it or diminishing it, has 
much to do with the question. At least it seems to assume that the 
normal position is due to the same physical causes as produce the devia- 
tions, and therefore I think that the deviations, whether of the polar or 
equatorial end, should be simply noted as east or west without regard to 
sign. In the southern hemisphere it is the equatorial end that we observe. 
Eegions where the north end is actually directed to the south, as at Port 
Kennedy and the Alert's winter quarters (1875-6), will require negative 
signs. 

10. It seems probable (1) that the mean position of the needle above 
referred to is always perpendicular to the direction of electric currents in 
the crust of the earth, or the atmosphere, or both, originating in a thermo- 
electric action of the sun on the meridian, and propagated north and south 
from the ecliptic ; (2) that the position of the meridian of the place, in 
reference to the sun, determines the direction of the mean deviation of 
the needle from its normal position or the mean solar-diurnal movement, 
and that the amount is determined by a balance of forces still to be clearly 
defined. The amount is known at a sufficient number of stations to test 
any law laid down. 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 1 3 

11. Ifc appears that so long as the sun is above the horizon of the place, 
there is comparatively little disturbance. In other words, the hours most 
habitually disturbed are before sunrise and after sunset. It is true that 
disturbances, once originated, display themselves simultaneously at dis- 
tant localities, irrespective of the hours of the day ; but the above seems 
to give probability to a conjecture that they originate in that hemisphere 
from which the sun is absent, and on those meridians which are at the 
time in the condition of greatest mean disturbance. 

12. Of known physical causes, the influence of sudden internal per- 
turbations analogous to those which become perceptible to our senses, as 
earthquakes and the like, seems to me the most nearly to meet the 
observed facts. They cannot be due to any atmospheric cause. Nor is it 
very probable that anything extra-terrestrial, such as solar perturbations, 
can operate with such vigour and suddenness upon our electric circula- 
tion. That there is a sympathy or correspondence between seismic dis- 
turbance and magnetic disturbance has been often shown, but I am not 
aware that it has ever been followed up in a comprehensive way. 

That this view implies some relation between the internal perturba- 
tions referred to, and the position of the part of the globe in which they 
originate in respect to the sun, as being in the hemisphere turned away 
from him, appears to follow, but I do not see any absurdity in such a 
supposition. 

13. Since continuous automatic registration affords a means of tracing 
the coi'respondence of either short-time or long-time movements with 
other observed phenomena, seismic movements, solar outbursts, auroral 
discharges, and atmospheric changes, for example such as no multiplication 
of eye-observations can do, this appears to me the first use to put it to. 
Forty years of eye-observation have added enormously to our store of 
facts, but brought us little if anything nearer a theory. Is it not time to 
try some other line of investigation ? 

14. With respect to the behaviour of the horizontal component during 
disturbances, depending as it does upon two variables, the dip and total 
force, it is rather unsatisfactory, but we have good and extensive data, 
and whatever principle of measurement or solution is applied to, the 
declination, must, I apprehend, be extended to this element. 

15. With respect to the vertical component I doubt whether the 
available data are as yet comparable in precision with those of the other 
two elements. I saw, however, some admirable curves at Toronto, pro- 
duced by Professor Carpmael's new instrument (I feel doubtful now 
whether they were curves of A Y or A0), which had all the character and 
freedom of those of the horizontal force, and when these have been worked 
np and discussed we shall know a good deal more about the influence of 
disturbances in increasing or diminishing the dip and total force. 



III. By Professor Schuster, F.R.S. 

I should like to submit to the Committee a few points to which their 
attention, in my opinion, might with advantage be directed. 

It is now nearly fifty years since Gauss applied the method of expan- 
sion in spherical harmonics to the elements of terrestrial magnetism. He 
considered his results only as preliminary, on account of the incomplete- 
ness of the data on which he had to work. 



74 EEPORT — 1885. 

We possess now so much more information on the mean value of the 
terrestrial elements at different places, that, it seems to me, a repetition 
of the calculations of Gauss would lead to valuable results. Such a cal- 
culation would not only be of theoretical importance. For we might in 
this way detect many points of interest, as, for instance, where if anywhere 
masses of iron are present near the surface of the earth in sufficient 
quantity to affect the magnetic elements. At such places we should ex- 
pect the harmonic analysis to give correct results only if extended to a 
large number of terms, so that if we confine ourselves, like Gauss, to four 
or five terms only, and find considerable differences between the calculated 
and observed values at some part of the earth's surface, we should have 
our attention specially directed to that part. 

It is only by a reduction such as that of Gauss that we shall be able 
to find out where we require further observations, and where a multiplica- 
tion of observations is unnecessary. 

It would be very desirable if we could extend the analysis of spherical 
harmonics to the daily variation of the elements and to magnetic dis- 
turbances generally. But it seems to me that if, as is likely, these changes 
are due to electric currents either above or below the earth's surface but 
near it, the analysis would have to be carried to a large number of terms 
before it would yield satisfactory results. But this, of course, is a matter 
which the actual calculation only can settle, and we ought therefore, at 
any rate, to make the attempt to apply the method of Gauss to the daily 
variation. With our present knowledge of that variation at different 
places of the earth's surfaces, there ought to be no difficulty in finding 
out whether five or six terms are sufficient to represeut it, taking ac- 
count, of course, also of those terms which have their origin outside the 
earth. 

Some observations of Sabine made near the magnetic pole " seem to 
point to the fact that part of the diurnal variation is due to a vertical 
component of an electric current crossing the earth's surface. Whether 
such a vertical component exists can be determined without difficulty, for 
we can actually measure it by taking the line integral of magnetic force 
at a given time over a closed curve on the earth's surface. 

I should like, therefore, to propose to the Committee to find out, in the 
first place, what determinations of the magnetic elements ought to be 
taken account of in the reductions. In countries where we possess a great 
number of accurate data, it would seem only an increase of labour to take 
account of all of them. On the other hand, where we possess few 
measurements we should in all probability have to use even approximate 
determinations. It is a point for the Committee to decide whether we 
ought to take the places which are to be included in the calculation spread 
as evenly as possible over the earth's surface, or whether a preponderance 
should be given to places near the magnetic poles or at other places of 
special importance. Also whether the more accui'ate observations ought 
to be weighed. Should the Committee approve of these reduction.=5, it 
would be well to ask at the next meeting of the Association for a sufficient 
grant to engage the assistance of one or two computers. 

I should like in conclusion to submit a few observations respecting 
the remarks made by Professor Balfour Stewart and Sir Henry Lefroy. 
The function of the Committee seems to me to be a double one. In the 

' See Encyclopedia Britannica — Terrestrial Magnetism (art. Meteorology). 



ON COMPAKING AND EEDUCING MAGNETIC OBSERVATIONS. 75 

first place, they are to discuss the best methods of reducing magnetic ob- 
servations ; but, before these methods can be put into execution, we must 
secure that the observations taken at different places are sufficiently 
homogeneous to admit of a common treatment. As we have to deal not 
with the individual observations, but with numbers which have already 
been reduced at the different observatories, it is clearly of importance that 
these preliminary reductions should be done everywhere in the same 
manner. Professor Stewart's suggestions refer exclusively to this point, 
while Sir Henry Lefroy rather discusses the question as to how the measure- 
ments already in existence can be made to yield information of physical 
value, and as they are treating of different matters, there does not seem 
to me to be necessarily any real difference of opinion between them. 
While agreeing entirely with a great many of the remarks made by Sir 
Henry Lefroy, I believe that some common method of reduction like that 
proposed by Professor Stewart is necessary before we can gain any know- 
ledge of magnetical disturbances. With regard to the proposals them- 
selves, the principal question will always be, whether the different heads 
of observatoi'ies can be made to agree on a uniform plan. The exact 
nature of the method of reduction is a matter which has to be settled 
chiefly by those who have practical experience in magnetic observatories. 
The method of rejecting disturbed observations, commented upon by 
Sir Henry Lefroy, is, no doubt, open to objection. If it was simply our 
object to gain information on the mean value of magnetic elements, no 
observation however much disturbed ought to be rejected ; but as soon as 
we suspect that the mean value is not the normal value — that is to say, 
that disturbances act more frequently in one direction than in another — 
we are necessarily driven to adopt some method of rejecting disturbed 
observations. The objections raised by Sir Henry Lefroy against the par- 
ticular method employed by Sabine seem to me to be, however, very 
serious, but I can see no difficulty in amending that method so as to 
render it free of the difficulty. 



IV. Letter from Professor 0. H. Darwin, F.R.S. 

Cambridge : 

June 10, 1885. 

A 'priori I should not have thought of distinguishing between mean 
and normal values, but I suppose that it is desirable to do so. It is 
obvious that if all the observations for a month are analysed, we get the 
mean harmonic constituents. Then if we recompute the values with 
these constituents (which may be done with a tide predicter), and sub- 
tract the hourly values from the observations originally analysed, we get 
a series of residuals. Supposing from those residuals we arbitrarily cut 
out a certain number which are above some arbitrarily chosen magnitude, 
and submit the rest to harmonic analyses, and supposing these presen1> 
us with a new series of constituents with pretty constant phases and 
amplitudes, then it would seem to me that we should be justified in the 
hypothesis that normal and mean are not the same thing. I must suppose 
that some process more or less equivalent to this has been carried out. 

I do not observe that any proposal is made to submit the monthly 
constants derived from harmonic analysis to a further analysis, and thus 
to derive the annual, semiannual, and terannual inequalities of the con- 



76 EEPORT — 1885. 

stituents. My meaning is tliat we ought to express the result in sets of 
terms of this form. 

Aq + A, cos e + A„ cos 2 + . . .1 

+ ai sin B + a, sin 2^+ . . . .]^^^ '? 

Bo + B, cos + Bo cos 2 e 4- . . . ■) . 
+ &i sin a + io 'sin 2 + . . . . / ^^^ ?* 

I had some time back a letter from Chambers at Bombay in which he 
says that he considers he has detected a lunar inequality. Now, unless 
this is certainly incorrect, is it not desirable to submit the quantities to 
analysis according to lunar time ? I take it that your proposal as to 
spherical harmonic representation is to put the Aq, Aj, A2, aj, ag, &c., 
as constants multiplied by spherical liarmonic functions of the latitude 
and longitude of the place of observation, Gauss had, as I fancy, only 
considered the mean values in this way, and you are proposing to treat 
the diurnal inequality in a similar manner. 

If much harmonic analysis is to be done, some form nearly like that 
used for tidal reductions would seem to be useful. 

The chief complication of those forms consists in the fact that the 
tide-heights are taken at exact solar hours, whereas we want measure- 
ments taken also at mean lunar and a number of other kind of hours. 
All this is avoided in your case, unless indeed you carry out an analysis 
for the alleged lunar influence. 

Yours sincerely, 

G. H. Darwin. 

V. 'Motes on the above Suggestions. By Professor Balfour Stewaet. 

The suggestions of the Committee are invited upon the following 
points : 

1. Do they agree with the suggestion of Dr. Schuster, that it is of 
importance to ascertain the solar-diurnal variation of the three magnetic 
elements at various stations of the earth's surface, with the view of treat- 
ing these after the method of Gauss ? 

2. Assuming that observations made at stations near the magnetic 
pole need special treatment, do the Committee think with Sir Henry 
Lefroy that even in ordinary localities the method of Sabine is objection- 
able for obtaining a correct value of the solar-diurnal variation ? As a 
good many declination observations have been treated by this method it 
is of importance to set the question at rest, and the suggestions of .the 
Committee are invited as to the best means of doing this. 

3. What do the Committee think of the herein-recorded method of 
obtaining the solar-diurnal variations in the case of the hoi'izontal and 
vertical force instruments ? I may state that a point of immediate 
scientific importance arises regarding the V. F. solar-diurnal variation, 
inasmuch as the observers at Lisbon and Bombay suspect that this, unlike 
the diurnal variations of the other two elements, does not vary with the 
state of the sun's surface. It would be very desirable to obtain con- 
clusive evidence of this from other stations. 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 77 



VI. Bemarlcs on Magnetic Reductions. By Senhor Capello. 

The method of the separation of the disturbances of the readings of 
the bifilar and the vertical force, of which I have sent a resume, and the 
examples of the calculation of the last year, seems practical enough to me, 
although it will give some trouble. It has, however, retained the prin- 
cipal fault, the arbitrary nature of the quantity which constitutes the 
disturbance. To practise this method upon the hourly observations of 
the vertical force is not, I think, more difficult than upon the bifilar. 

With respect to the vertical-force instrument of this observatory, I do 
not find it very inferior to the bifilar, except for some months on two or 
three occasions, during which the equilibrium position was not good, for 
the curves had shown a jumping motion ; otherwise it has answered 
almost as well as the bifilar, notably in the three or four last years, 
where the coefficient of temperature is very much reduced by the adop- 
tion of a contrivance to compensate the effects of temperature. 

Our photographs already embrace twenty-one complete years. The 
meteorological work, and the care connected with the administration of 
the observatory and the meteorological stations absorb the greater jiart 
of our time. The reductions of the magnetic observations are very much 
behind, and it would be difficult to advance simultaneously all the 
elements as they should be ; therefore I think that it would be convenient 
to establish an agreement upon the work which by preference it is de- 
sirable to accomplish, and for what period for a general comparison. 
With regard to No. 7 of the suggestions of Sir J. H. Lefroy, I am en- 
tirely of his opinion, and I will add my ideas upon some researches that 
I think would throw light upon the causes of the disturbances. 

1. In a paper by Messrs. Capello and B. Stewart (' Proc. R. S.,' January 
28, 1864;) upon a first comparison of the disturbances at Kew and at 
Lisbon, we have recognised that of the little and abrupt disturbances of 
three to five minutes' duration (which are called peaks and hollows), and 
which are seen simultaneously in the three curves, those of the decli- 
nation and of the vertical force are in the same direction at Kew and in 
the contrary direction at Lisbon ; that is to say, while tho north end of 
the declination needle at Lisbon goes towards east the same end of the 
vertical-force instrument dips. The contrary happens at Kew, the north 
end of the declination needle going towards east, while the same end of 
the vertical-force raises itself. 

Again, on the other hand, we have also recognised the agreement of 
the behaviour of the peaks and hollows of the declination curves at Kew 
and at Lisbon. Thus one vertical peak at Lisbon corresponds always to 
a hollow at Kew, and vice versa. It would be interesting (1) to extend 
this research upon peaks and hollows further ; that is to say, between 
more distant observatories, employing the utmost rigour possible in the 
time-measures, in order to recognise if the times of the appearances of 
the peaks are absolutely the same, or if there is a sensible difference in 
the most distant observatories. (2) Again, we ought to look in some 
observatory immediately between Lisbon and Kew in order to see if the 
vertical-force peaks correspond sometimes to the peaks, sometimes to 
the hollows of the declination. 

2. For the study of the disturbances I think it would be necessary 
that each observatory furnished with magnetographs should make pro- 



78 KEPOET — 1885. 

jections upon tbe plaue perpendicular to the inclination-needle, of the 
movement during tbe disturbance of tbe dipping pole of sucb a needle 
supposed to be suspended without friction by its centre of gravity. ^ 

This projection ought to be constructed by means of the declination 
variations ( A<i) and those of the inclination (At) ; the first being multi- 
plied by the cosine of the inclination (cos /), in order to its reduction in 
the inclination direction. 

The readings of the thi-ee curves being made at the time of the first 
meridian, chosen at intervals of 2 m., 3 m., or 5 m., according to the 
deo-ree of precision which is desired, their differences are taken by com- 
parison with the first reading, and these differences should be reduced 
according to the values of the coefBcients. In combining the values of 
the movements of the vertical force and of the bifilar, we find by the 

known formula (^ At=3in icosiY -^ _ -^ j J the variations of the incli- 
nation ; these variations are projected upon the chart in vertical directions, 
havino' reference to the first reading, and those of the declination in 
horizontal directions, employing a convenient scale. 

Here is an example: — Four hours of the disturbance of the 1st of 
February, 1881, Oh. to 4 h. (time of Pawlowsk) at Kew, and Lisbon 
readings being at the intervals of five minutes. 

It is noticed that all the movements are reproduced in the two figures. 
They are generally at great length, and now and then deformed at Kew 
and of different inclination by comparison with the horizontal line. 
All the movements at Lisbon and Kew are executed in the manner con- 
ti'ary to the hands of a watch. The aspect is sooner at Kew. 

If Ave make a similar research upon other more distant observatories — 
for example, Pawlowsk and Toronto — the same movements are still re- 
marked ; but some aspects are completely deformed, the movements at 
Toronto being executed in the manner of the hands of a watch. 

The measurements in these researches have been taken from the 
curves of a scheme of a study of Mr. Wild upon the disturbances of 
February 1, 1881. 

VII. Observations on Magnetic Reductions. By Dr. H. Wild. 

As Messrs. Balfour Stewart and Brito Capelloin the ' Suggestions for 
the Committee on Magnctical Reductions,' as well as Herr T. P. van der 
Stok in the ' Communications of the International Polar Commission,' 
No. 109, have clearly shown, there are to be distinguished in the varia- 
tions of the magnetic elements — 1st, their normal daily periods ; 2nd, 
the slow and constant changes which the absolute values of the days' 
means of these show ; 3rd, the eventually different daily periods which 

• I think that it would be possible to construct a very simple instrument which 
could well register b)- photography all such disturbances, which would make these 
researches less laborious, avoiding all the measures and reductions which are alwaj's 
laborious. Let a little needle be suspended conveniently by the centre of gravity, 
employing a thread of silk. In one point of this needle let there be a mirror per- 
pendicular to its magnetic axis. A luminous slit might be made to fall almost 
perpendicularly upon the mirror, registering the movement in all the directions of 
the needle. In order that these movements should not be confounded and super- 
posed, the registering cylinder should proceed by jerks from hour to hour, or of tener 
according to experience. 



ON COMPARINa AND KEDUCINa MAGNETIC OBSERVATIONS. 79 

the deviations from the normal daily path show.' In how far we are to 
conceive of the two last variations as disturbances must, in my opinion, 
be decided by experience. 

In any case we require, for the fixing and estimation of these last varia- 
tions, a distinct starting point, which the normal daily path may present. 

It is, therefore, specially important here to establish this normal daily 
path of the magnetic elements. Now regarding the method which Sabine 
has devised for this, and also used so much, there is, in the first place, 
displayed what Lefroy, Weyprecht, and others have made so prominent, 
the arbitrary nature of the limits which are assumed for the expulsion of 
the so called disturbed data. Among the different proposals which have 
been made for a rational fixing to these limits the most worthy of notice 
is that of Buys Ballot, in which these limits are to be set where the devia- 
tions begin to show another period. Van der Stok has distinctly modified 
the Sabine method for the discovery of the normal daily path. His 
altogether very complicated method suffers, in my opinion, from the same 
wide evils as the Sabine method, viz., that it proceeds from the daily 
paths, derived, like them, from the sum of all observations without dis- 
tinction, i.e. including disturbances. Now it is evidently, as Weyprecht 
has already shown, impossible out of the so procured data to get rid alto- 
gether of the influence of the disturbances on the normal daily path, if 
these are not quite irregularly distributed over the day, but are all subject 
to a certain daily period. Lefroy again, in his working out of observations 
at Tort Simpson and Lake Athabasca, has not employed all the data for 
the deriving of the first hour's means, but only the days and hours which, 
according to him, wei-e not to be regarded as disturbed, i.e. where the 
amplitude of the movements does not go beyond a certain limit. The 
fact that the exclusion of these movements is not settled through the 
criterion of Buys Ballot on the one hand, as well as the consideration, on 
the other, that days with not less amplitude of movement may also be 
disturbed, because the disturbed periods might unite with the normal 
periods, so as to weaken themselves through interference (which, as we 
shall see, is partly the case), prevents the method from being satisfactory. 
In the Programme and in the Sittings of the fourth International Polar 
Conference in Vienna (April 1884) I have given out and developed a 
new method for the derivation of the normal daily path of the magnetic 
elements (see ' Communications of the International Polar Commission,' 
No. 94, p. 199 ; No. 97, pp. 208, 211 ; No. 98, pp. 254, 255, 257, 258), 
■which is supported by the observation that in the magnetograph traces, 
even at the epoch of maximum disturbances, in every month are to be 
found a number of days in which a quite regular, and also as regards 
these days concerned a recurring periodical path is distinctly recognised. 

I regard these days as days with undisturbed daily paths, and the 
hourly means of all these days as representative of the normal daily path 
of the elements concerned in the month in question, according to its 
relative as well as to its absolute size. The selection of these normal days 
may from the first likewise seem very arbitrary ; in practice, however, 
this is not the case, as hardly a doubt can arise as to which days are to 
be taken, and besides the result will not be very distinctly different 
whether one chooses one or two days more or less, if from the first one 

'For the sake of simplicity I have spoken here only of the daily periods ; clearly 
for the remaining periods also, which show the variations of the earth's magnetism, 
suitable distinctions can be made. 



80 REPORT — 1885. 

only takes the precaution to eliminate through linear interpolation any 
sudden and individual disturbances which in such days at times 
show themselves. The differences of all the observed data from the so 
obtained values of the normal daily path in each month I regard as 
deviations from the normal, eiSected by some disturbing circumstances. 
Should, e.g., all these deviations for all hours' values be put in the form 
of a table, and should each be distinguished as positive and negative, 
either by certain signs or, according to Balfour Stewart, by different 
colours, we should recognise at once, from the similarity of the signs and 
the nearly similar size of the figures, whether a day was disturbed uni- 
formly positive and negative, and from the recurrence of the positive 
figures at certain hours, and negative in certain other hours on different 
days, whether the disturbance points to a new period different from 
the normal daily periods. In order to establish these conclusions with 
numerical correctness, it is best to group the deviations according to their 
extent, separating negative and positive, and then to investigate their 
periodicity as Buys Ballot has proposed. 

Herr D. Miiller has worked out according to these principles the 
jottings of the magnetogi'aph in the Observatory of Pawlowsk for the 
period of the International Polar Expedition, August 1882 to August 1883. 
His important results have been laid by me befoi'e the Imperial Academy 
of Science, May 21 and June 2, 1885, and are at present published 
in the ' Repertoriura for Meteorology.' Without entering into the details 
of Herr Miiller's results, I only remark that the success of the first 
attempt seems to speak well for this method. The course of the contained 
normal daily path in the separate months has unexpectedly become regular 
for all three elements — declination, horizontal and vertical intensity, and 
also for inclination and total intensity. The days' means of the normal 
days show proportionally small differences, and only the greater devia- 
tions have a pronounced different periodicity, which again is different for 
the positive and negative. Herr Miiller has therefore only pointed out 
the latter as disturbances, and the former as simple oscillations about the 
normal path. For two months, October 1882 and March 1883, I have 
prepared a compai'ison of Sabine's method for the declination with that 
got by Miiller from my method. Here, in the calculation according to 
Sabine, + 2 is assumed as the limiting value for the expulsion of dis- 
turbances ; and these operations for individual hours were repeated as 
often as eight times. In spite of this, there is shown by a glance at the 
enclosed table that even by the Sabine method the influence of the pre- 
vaihng positive disturbances late in the forenoon, and of the maximum of 
the negative disturbances in the afternoon, could not be eliminated from 
the result. I have the intention to get worked out according to this new 
method, which, in short, is applicable to all these data, certain traces of 
magnetographs in St. Petersburg and later in Pawlowsk from 1870, and 
have for this purpose for the whole period chosen the normal days out of 
the photograms. 

From this came the unexpected result that the number of these at the 
time of the minimum of the sun spots is not so much greater than at the 
time of the maximum. 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 



81 



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VIII. Letter from Sir Frederich Evans to Professor Steivart. 

21 Dawson Place, Bayswater, London, W. r 
Mai/ 0, 1883. 

Dear Professor Balfour Stewart, — I stall be glad to render the 
Magnetic Committee all the assistance in my power, but I have been much 
out of sorts in my health for some time, and cannot so well undertake 
any work requiring much application. 

On Tuesday I leave London for a few days, and will take the papers 
with me you forwarded on the 6th instant. 

Until we see our way more clearly, it is the discussion of the dis- 
turbances of the Declination needle which appears to me the most im- 
portant to break ground upon. On a clear insight of the probable laws 
at a few selected stations in both hemispheres, a discussion of other 
elements might well follow. Too grand a scheme and complicated 
methods of research would, I fear, break down. Sabine's methods had, at 
least, simplicity to recommend them. 

A letter to the above address will reach me. 

Yours faithfully, 

Fredk. Jno. Evats^s. 



IX. Letter from the Astronomer Eoyal to Professor Stewart. 

Royal Observatory, Greenwich, London, S.E. : 
Jtili/ 8. 

Dear Prof. Stewart, — The printed suggestions for the Committee on 
Magnetical Reductions arrived at a very busy time, and since then I have 
been away fi-om home ; hence the delay. 

As there is some diflBculty in discussing abstract questions, I think 
it would save misunderstanding if you would make your suggestions with 
reference to our Magnetical Results for 1883, now in the press, of which 
I send you a copy. There are several additions and alterations which I 
have introduced in consultation with Mr. Ellis, in order to give as much 
information as practicable about the magnetic curves. We now give, in 
addition to mean values of the magnetic elements for each day and the 
mean diurnal curves for each month, the daily range, i.e., the amplitude 
of the diurnal curve for each day, and particulars of all disturbances, 
small as well as large (either in the notes or in the plates). Harmonic 
analysis also has been applied to the diurnal variations for each month 
and for the year. 

Now the question is, how far the suggestions of the Committee are 
carried out in the results given. As for rejection of disturbances, I am 
inclined to agree with Sir Henry Lefroy in his objection to Sabine's 
mode of treatment. At Greenwich the practice has been to draw a 
pencil curve smoothing down the irregularities of the trace, and to reject as 
disturbed those days for which a continuoiis pencil curve, agreeing gene- 
rally in form with the normal curve, could not be drawn through the trace. 
I see no reason to modify this. 

Yours very truly, 

W. H. M. Chkistie. 



ON COMPARING AND KEDUCINa MAGNETIC OBSERVATIONS. 83 

X. Letter from George M. Whipple, Esq., to Professor Stewart. 

Kew Observatory : 

Juli/ 29, 1885. 

Dear Prof. Stewart, — I have carefully read the paper you were so 
good as to forward to me, ' Suggestions for the Committee on Magnetical 
Reductions,' and must confess that I am in most points fully in accord- 
ance with Sir H. Lefroy. 

I would much rather trust to the solution of the various problems of 
Terrestrial Magnetism by a farther and more extended series of com- 
parison of curves than by an extension of numerical processes. 

The reduction of the Fort Rae observation shows how enormously 
large and frequent the variations may be in some parts of the earth ; 
and such being the case, I fail to see how any nseful purpose could be 
served by the repetition of the calculations of Gauss. 

I think that magneticians should endeavour, if possible, to enter into 
communication with geologists and seismologists, and endeavour to trace 
out clearly the causes of (what I would term^) superficial variations, pro- 
bably due, Prof. Schuster says, to electric currents, for localities well 
furnished with magnetic obrscrvatories, such as Europe, rather than to 
attempt at once to solve the whole problem of distribution throughout the 
earth of magnetic matter. I am, yours faithfully, 

G. M. Whipple, Superintendent. 

P.S. — I enclose also copy of some remarks addressed by Capt. Dawson 
and myself to the Vienna Congress on the subject. 

Further and additional remarlis on the questions to he submitted to the 

Vienna International Polar Conference. 

We are of opinion that careful inspection of the observations them- 
selves will suffice to show the days and hours when the diurnal curve 
follows its normal course. From days and hours selected by this inspec- 
tion, mean curves may be obtained, and nltimately by interpolation a 
series of hourly values may be arrived at for every day in the year. 

Readings differing from these values by more than a certain separat- 
ing value should be set aside and discussed as disturbances. It appeal's 
to us probable that the principle of determining the mean monthly diurnal 
curves for each station from observations selected only on such days as 
are shown by evidence of magnetographs elsewhere to have been mag- 
netically calm, assumes beforehand a uniformity of magnetic conditions 
over the globe, and might, therefore, fail at certain stations. A rough 
comparison of Port Rae and Kew Observatory results indicates to us that 
it is rather more advisable to deal with hours and not with days as a 
whole, and that therefore some rule, either Sabine's or Lloyd's, must of 
necessity be adopted. 

There seems no objection to the application, first, of Lloyd's rule to 
throw out disturbances, and then to the subsequent classification of these 
disturbances after the method suggested by Wild. 

We fail to see as yet any method of introducing possible corrections 
for sun-spot periodicity into observations made during so short an inter- 
val of time at stations where no previous observations have been taken ; 
and therefore recommend that this disturbing element be omitted entirely 



84 REPORT — 1885. 

fi'ora the proposed international discussion, and left entirely to specialists 
for subsequent treatment. 

With regard to the discussion of disturbances, we would suggest that 
each expedition should draw up a list of the days, selected according to 
Gcittingen time, considered by them a disturbed day, and then from a 
comparison of such lists the Conference should decide on what days 
should be selected for particular discussion in addition to the term days. 

Question 3. — Dr. Wild's suggestion as to plotting the curves is so 
very convenient that we have already adopted it in making preliminary 
curves of the Fort Rae observations. It will be necessary in addition, 
however, to decide upon the scale of abscissa} to be used for the 2U- 
secoud interval observations on term hours. We suggest the employment 
of a scale giving six minutes of abscissaj to each minute of time. 

Questions 4 and 5. — The conversion of Gaussian units into those of 
the C.G.S. system is so simple that it is unnecessary for the Conference 
to disturb the existing historic system. The Kew Observatory has already 
for years published their results in both systems. The foot-grain system 
is rapidly becoming obsolete, most magnetometers now constructed having 
metre instead of foot scales. 



XI. Letter from General Lefroy to Professor Stewart. 

82 Queen's Gate, S.W. : 

Jiili/ 15, 1885. 

My dear Professor, — I have carefully read, and return herewith, the 
papers of Senhor Capello and Dr. Wild. I have difficulty in attaching 
a physical idea to the ingenious method of projection proposed by Senhor 
Capello. He gives the movement, projected on a plane perpendicular to 
the dip of the axis or intersection of the plane of dip and the plane of 
declination ; but I do not see how the variations of total force are to be 
shown in conjunction with this, or with what physical notions to connect 
the resulting curves. The actual realisation of the suspension of a 
needle by its centre of gravity without friction in any direction, especi- 
ally if counterpoised to carry a mirror, would be a great achievement, 
b'at, with great respect, I doubt its being possible. Still his comparison 
of Lisbon and Pawlowsk is very curious, and strongly conflrms my belief 
that, be our stations few or many, the results at all of them must be 
brought into one view, by identity of treatment and prompt circulation, 
to obtain a clue, and to effect this we want a Bens ex machina. 

My file of bulletins of the International Polar Commission does not go 
beyond Part 5. I have not seen Herr van der Stok's communication, which 
Dr. Wild refers to. It has occurred to rae, following a hint of Lloyd's,' 
that the area of movements would be a good measure of the forces pro- 
ducing them, and that it might be possible by an instrument on the prin- 
ciple of Amsler's planlmeter to integrate these areas for the whole 
twenty-four hours, or any not very small portions of it, in moderate dis- 
turbances. The extremely active ones would not be easily measurable. 
To take cognisance, as has sometimes been done, of those movements 
only which coincide with hours of mean time or Gottingen time, appears 
to me to forego the special advantages of continuous recoi'd. I agree 
with Dr. Wild that there is no difficulty in selecting the normal days at 

' Trans. R.I.A., vol. xxii. 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 85 

any station, but whether they -woulcl be the same at other stations has 
not, as far as I know, been ascertained. Lloyd, as you know, worked out 
the consequences of adopting every possible value of disturbance test. 
Sabine has given two or three values, all purely empirical. If my plan 
of areas were practically feasible, it does seem to me free from that ob- 
jection. Dr. Wild appears to disregard magnitude, and to refer all the 
observed data to his normal values, and I think nothing less comprehen- 
sive will be found satisfactory in the long run. It is gratifying, however, 
to find that his results are not widely different from those obtained by 
Sabine's method. As Dr. Wild quotes Toronto, I suppose that some 
hmited circulation and occasional comparison does go on, but Carpmael 
has no staff to keep it up regularly. We all want more hands, which 
means more money. 

Believe me faithfully yours, 

J. H. Lekrot. 



XII. Observations, S,c. By Chakles Chambers, F.R.S.. 
Superintendent, Colaba Observatory, Bombay. 

There can be little doubt that the activity displayed during the last 
quarter of a century in the record of the phenomena of terrestrial mag- 
netism was induced mainly by the interesting results to which Sabine 
was led in his discussions of the observations of the British, colonial, and 
other observatories ; that it was in the hope of extending and completing 
such results by wider observation, that men of science in all parts of the 
civilised world urged upon their respective Governments the advisability 
of establishing magnetical observatories. Few who have studied Sabine's 
memoirs — displaying, amongst other remarkable generalisations, the out- 
lines of a system of the globe in respect of the regular solar diurnal 
variations and the variations of these with the season of the year, and 
connecting with the sun-spot period variations of the range of the regular 
diurnal variation of declination and of the aggregate amounts of dis- 
turbance — will doubt the wisdom of the influence thus brought to bear 
on the guardians of the public purse, nor, whatever else may be done, of 
the propriety of carrying the work to the legitimate conclusion of extend- 
ing and completing Sabine's results. To act otherwise, in the absence of 
a physical theory to which there is as yet no clue, would be to admit a 
change of judgment which there is nothing in the circumstances of the 
present day, any more than there was at the time when the work of auto- 
matic registration was initiated, to justify, and would, moreover, be to 
discourage the statesmen who, by the provision of funds, have aided in 
the production of records of the crude phenomena, from making farther 
sacrifices in that direction : these dignitaries would, in their capacity of 
trustees for society, rightly complain that they had been led to expect 
systematised knowledge, but had been given instead piles of records of 
unused facts, and that the responsibility and expense of preserving these 
is scarcely a substitute for the reward they had been dazzled with the 
promise of. 

2. In my opinion the scientific authorities, on whose advice much 
money has been spent in procuring many years' continuous records, are 
bound in honour to see that the representations which induced the various 
Governments to provide funds are justified by at least a full carrying out 



86 REPORT — 1885. 

of tlie original purposes as to tlie uses to which the records were to be 
applied. 

3. The fact is that funds have been expended too exclusively upon 
material appHances, and upon agency for working them : the statesman 
can understand that his country gets a tangible return when observa,tory 
buildings, instruments, operators, records, and reports appear before him 
as a result of the grants that he makes ; but it is for the man of science, 
the original adviser, to make him understand that these are very delusive 
results unless supplemented by appropriate measurement, computation, 
and discussion. 

4. And this is the more important inasmuch as the cost of utilising 
the records, even up to the point suggested by Sabine's examples, will 
at least equal the amount that has been expended in their production. 
It is indispensable that inexpensive measuring, copying, and computing 
power should be used, under skilled direction, on a large scale ; and here 
it is that the main part of the cost arises. It would be simple waste of 
superior energy to set a cultivated physicist to the appalling task of per- 
forming the simple but multitudinous series of operations thatai-e involved 
in any adequate treatment of the observations ; and it is to the insufficiency 
of suitable agency in the working power of existing observatories that is 
probably to be attributed the fact that so little has yet been done in the 
way of independent reduction and discussion of the records of the auto- 
matic magnetic instruments. That the work before us is laborious and 
costly is, however, no argument against the undertaking of it if we have 
reason to believe that an adequate return will be obtained ; and a more 
costly process is to be preferred to a less costly one if the quality of the 
results that are the outcome of it is higher in a corresponding degree. 

5. I cannot but think that the wonderful progress made during the 
last century in the experimental sciences is apt to make us unduly im- 
patient of the necessarily slower progress of the observational sciences. 
If astronomy had, during the progress of observation, to have its period 
of phenomenal generalisation — its Ptolemy, its Copernicus, its Kepler— 
before light as to the mode of physical causation dawned upon its 
Newton, is it much to be wondered at that a much more complicated 
science, as terrestrial magnetism undoubtedly is, should have to pass 
through its period of discoveiy of general phenomenal relations — relations 
which the physical theory will ultimately have to explain — before the 
conditions essential to the conception of a general theory can be laid 
down ? 

6. It will be seen that whilst I have no faith in the flights of genius 
that would look at the crude facts as nature presents them to us, and 
from such comj^lex data devise a theory to unravel the complexity, I have 
the greatest confidence in appropriate methods of analysation as leading 
to relatively simple jDhenomenal generalisations, and thence, inevitably in 
the long run, to the desired physical theory. The first step to be taken 
should, I think, be to collect together all accessible results that have 
already been worked out and published of the nature of — 

(1) The regular solar-diurnal variations; 

(2) The disturbance variations — diurnal, annual, and secular ; and 

(3) The lunar-diurnal variations ; 

and to convert the expression of them for each of the elements, declination, 
horizontal force, and vertical force, as far as available, into metre-gramme- 
second or C.G.S. units of force. If not already done, the averages of 



ON COMPABINa AND EEDUCINa MAGNETIC OBSERVATIONS. 87 

{1) should be calculated for each month from the separate results of all 
the years that are available, and curves be constructed to represent these 
average monthly variations according to time-scales and force-scales which 
would be marked on the curve-forms. It would be convenient that the 
curves should appear, for any one station, in a row, beginning with 
January, on a long narrow slip of thick paper, so that the sets of curves 
for any one station might be placed close under those of any other 
station for easy comparison. For preservation, the slips of paper would 
be kept in a portfolio, not bound into a book. Curves on a less elaborate 
scale, as would be suggested by the meagreness (or fulness) of the 
materials collected, might similarly be constructed on slips to represent 
the variations (2) and (3). Such series of curves, to the extent to which 
data for them would be found easily accessible, would, I imagine, con- 
stitute a conclusive answer to those who doubt the utility of extending 
investigation in the same direction ; but, taking continuity of change of 
character of the variations in passing from place to place as a criterion 
of the value and importance of the results obtained, they would also 
serve the further purpose of suggesting whether and where Sabine's 
methods are exact enough, or to what extent the application of even more 
laborious processes of reduction would be justified. These curves should 
be lithographed on thick slips of paper, and distributed amongst the 
directors of observatories and other students of terrestrial magnetism ; 
and, as little in the shape of description or comment need accompany 
them, the originals could be produced by agency of an order that should 
be readily obtainable, and that would require but little supervision, from 
some specialist member of the Committee. 

The curves might, with advantage, be accompanied by a table of the 
absolute values of the elements declination, horizontal foi'ce, and vertical 
force for each station ; and also by tables of ranges of the solar-diurnal 
variations of each element on the average of each full year. 

7. It has been well established by Broun and myself that the so-called 
lunar-diurnal A^ariation is a function both of the season of the year and 
of the age of the moon, and there is reason for believing that the bulk of 
the phenomena is really a part of the regular solar-diurnal variation, a 
part that reverses its character four times in the course of the lunation. 

Now the adoption, by Sabine's process, of a uniform solar-diurnal 
variation for the whole of a calendar month, whilst perhaps accurate 
enough for the determination of the general character of the disturbance 
laws, leaves much to be desired when the object we are in quest of is a 
minute variation which has, in the case of the declination, a less range 
than a single minute of arc, and which is subject to variation of character 
with change of season. Here we require that a mean solar-diurnal 
variation should be calculated for each individual day, in order that the 
elimination of mean solar effect should be nearly complete ; and knowing 
that either a part of the solar-diurnal variation, or the bulk of the lunar- 
diurnal variation, runs through a cycle of change in a lunation, the best 
period for which to calculate the daily means is a mean lunation, or the 
nearest odd number of mean solar days to a mean lunation — that is to say, 
twenty-nine days. The importance of this period should be kept in view 
from the first, whether or not there is any immediate purpose of investi- 
gating the lanar-diurnal variations, and my present object is not so much 
to advocate the inclusion of such investigations in the first general 
scheme of operations as to explain why the period of twenty-nine days 



88 REPORT — 1885. 

enters into modiScations that I would suggest of tlie procedure proposed 
by Dr. Balfour Stewart in dealing witli the horizontal force tabulations, 
Taut whicb modified process should, I think, be applied also to the de- 
clination tabulations. 

It is not a general rule that the hours at which the bulk of disturb- 
ance occurs are the same for both the elements declination and hori- 
zontal force ; and hence — thougb it is liighlj probable that distui-bance 
of some degree in one element occurs on the same day as disturbance of 
another degree in the other — we cannot with safety allot the disturbances 
to identical hours. 

8. First, I would substitute for Sabine's classification of disturbances 
as 'larger' and 'smaller,' a division into tho.se that ai'e without the 
limits set by the normal ± the separating value, and those that are 
within those limits ; and instead of rejecting disturbed observations I 
would, at such step of Sabine's process for separating the larger dis- 
turbances, replace each disturbed entry by the same number minus the 
disturbance without the limits — as apparent at that stage. The dis- 
turbances without the limits would be separated and the laws of their 
variations determined by the methods that Sabine applied to his larger 
disturbances, but the disturbances within the limits would remain in- 
volved with the regular variations until a late stage of the investigations. 

9. Secondly, as regards jirogressive change in the readings, both of 
the declination and horizontal force instruments, it would, I think, gene- 
rally suffice to treat that change as uniform during the course of a month. 
Having entered the hourly tabulations for a given month on a table 
(A call it) having the hours marked at the top of the columns and the 
days of the month in the first or left-hand column, and having taken 
daily means, I M'ould take the mean of the first fifteen of those daily 
means and the last fifteen of the preceding nionth's table A as the mean 
number for the beginning of the month ; and similarly the mean number 
for the end of the month would be the mean of the last fifteen daily means 
of that month and the first fifteen of the next following month. Change 
at the uniform rate indicated by the mean numbers ' for the beginning 
and end of the month I would eliminate from the original hourly tabula- 
tions of table A, and enter the new number on a new table (B), to which 
I would proceed to apply Sabine's (modified) process. This would lead 
to a general knowledge of the regular solar-diurnal variations for each 
month, and of the laws of the disturbance variations ; and here a rest- 
ing-place might be found if it were desired to compare results from 
different stations before proceeding with more elaborate reductions. 

10. To proceed, however, I would next, having obtained the amounts 
of disturbance without the limits, eliminate these amounts from the re- 
spective disturbed observations of table A, calling the table thus altered 
(A'), and this table should form the basis of discussion in respect of the 
regular solar-diurnal variations for each day, the lunar-diurnal variations, 
and the laws of variation of disturbances within the limits. 

From table (A'), and the corresponding table of the preceding and 
following months, I would construct another similar table (C),each entry 
in which would be the 29-day mean of the numbers for the same hour 

' The effects of disturbances without the limits on the daily means I would take 
to be sufficiently indicated by the departures of those means from corresponding 
daily means, as calculated from the mean numbers for the beginning and end of the 
month, with a uniform rate of change from one to the other. 



ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 89 

in table (A'), viz., of the numbers for the day of the entry and the four- 
teen preceding and fourteen following days. The numbers of table C 
for all the hours of a given day we may take to represent very approxi- 
mately the mean solar-diurnal variation — flus a constant — for that day, 
the average extending over the lunation of which that day is the middle 
day. They will be affected by progressive change of the values of the 
tabulations, and by disturbance within the limits. 

11. Lastly, the excesses of the numbers of table (A') over the corre- 
sponding numbers in table C, fJus a constant round number,^ should be 
entered on a fourth table (D). The numbers of this table, which will be 
affected only by that part of the solai'-diurnal variation which goes 
through a cycle of change in a lunation, and by disturbance within the 
limits, we may proceed to arrange in new tables with reference to the 
moon's age and the season (or month) of the year,^ and so determine 
the character of the variations which the luni-solar-diurnal variation is 
subject to. Having done this, a further elimination will put us in pos- 
session of residual numbers, the variation of which must be attributed 
solely to disturbances within the limits, and may be studied and the 
numbers be manipulated accordingly. 

12. I agree with Dr. Balfour Stewart that the time has not yet 
arrived for laying down rules for the treatment of the vertical force 
tabulations. 



XIII. Letter frovi the Eev. Professor S. J. Ferry, F.B.S. 

Sej)temhcr 8, 1885. 

Dear Dr. Schuster, — I have read over the Report Dr. Stewart kindly 
forwarded, and I cannot help thinking that our first step should be to 
collect the results already obtained for the Daily Range of the Declina- 
tion, reduce the means already worked out to a common scale, and then 
distribute the whole in a tabular and in a graphical form. Much might 
be learnt from seeing these results in a collective form, and we could then 
better judge how far processes more laborious than those of Sir Edward 
Sabine are like to repay the labour. 

If all observations are made use of in deducing the Daily Mean Ran^e 
the Disturbance period will certainly interfere with the Solar Diurnal 
Range, and if we pick out quiet curves in which the Daily Range is well 
marked, we are very liable to give undue weight to variations in the 
Daily Range which are independent of ordinary disturbances. 

Yours very truly, 

S. J. Perry. 

' The constant round number is added to avoid the inconvenience of having tO' 
deal afterwards vf ith jwsitive and negative numbers. 

- If a separate table be allotted to each day of the moon's age, the resulting 
mean variations will be practically the same whether the hours refer to the solar or 
the lunar day ; and as the numbers available are for the exact hours of the solar day, it 
is convenient to let the arrangement of the table be for the solar day rather than for 
the lunar day. 



90 EEPOET — 1885. 



Report of the Committee, consisting of Professor Crum Brown 
(Secretary), j\Ir. jNIilxe Home, Mr. John Murray, and INIr. 
BucHAN, appointed for the purpose of co-operating with the 
Scottish Meteorological Society in making Meteorological Obser- 
vations on Ben Kevis. 

Dl'Ring tlie past twelve montlas the observatious on Ben Nevis have 
been made every honr, by night as well as by day. This remarkable 
continuity in the observations, conducted under such great difficulties, is 
due to the enthusiasm and undaunted devotion to the work evinced by 
Mr. Omond and his assistants, and to the completion of the Observatory 
building last summer with its tower, which admits of a ready egress 
from the Observatory when the doors are blocked with rapidly accuma- 
lating snow-drifts, except during those rare occasions, of which the winter 
months of 1884-85 afforded only one example, in the great storm of 
February, when from 6 p.m. of the 21st to 8 a.m. of the 22nd no light 
could be carried in a lantei-n outside to the instruments. This inter- 
ruption refei's only to the observations of the temperature of the air. 

During the year the most notable additions made to the observations 
refer to the I'ainfall and the wind. The actual precipitation — rain, sleet, 
snow, or hail — has been collected with rain-gauges specially designed for 
the purpose, and measured with the greatest care every hour since 
June 24, 1884, with, it is believed, a very close approximation to the 
truth ; and the hourly results for each month have been calculated. 

In the end of October the anemometers designed by Professor 
Chrystal for the Observatory, to register continuously the velocity and 
direction of the wind, were added to the observing instruments. Unfor- 
tunately, however, in tlie colder months of the year the deposition of 
ice-crystals, which Mr, Omond has described in a recent paper, renders 
all anemometei's quite useless, except at rare intervals. During the 
seven months from November 1, 1884, to May 31, 1885, there was only a 
mean of thirty days in which the anemometer Avas in working order. 
During these days the greatest velocity was on the night of April 24-25, 
w^hen for twelve hours the mean velocity was seventy-four miles, rising 
one hour to eighty-one miles. 

Estimations of wind-force have continued to be made every hour 
during the year, and the results show, as in the previous year, that the 
wind is above the mean daily force during the night and below it during 
the day. The maximum occurred from 2 to 3 a.m. and the minimum 
from 2 to 3 p.m., the difference between the extremes being between two 
and three miles an hour. The means of the observations made since the 
Observatory was opened show that the same relation holds good during 
each of the four seasons. These peculiarities in the diurnal variation in 
the velocity of the wind on Ben Nevis are of the greatest importance, 
especially in view of similar curves obtained at other high-level obser- 
vatories situated on mountain peaks, and by Mr. Archibald Douglas from 
his balloon observations and experiments, and their bearing on atmo- 
spheric movements. 

During July 1885 the anemometers have been continuously at work, 
and there are now before us a month's complete hourly records of 
recorded velocities and estimated wind-force. The curves drawn from 



ON METEOROLOGICAL OBSERVATIONS ON BEN NEVIS. 91 

the results of these two methods are closely congruent. This double set 
of observations supply the data for a more exact conversion of the 
estimations of wind-force, according to Beaufort's scale, into their equiva- 
lents in miles. A large number of similar observations made on boai-d 
the Challenge!- also form a valuable contribution to this inquiry. So 
far as the observations go, they appear to indicate that the equivalents in 
miles usually given for the higher numbers of Beaufort's scale are too 
small. From 8 to 9 a.m. of August 9 the anemometer registered 
86 miles, and during this hour the estimated force was from 8 to 9 
of the scale. The equivalent in miles for this force, provisionally 
adopted by the Meteorological Council, is from 48 to 56 miles. What is 
the number of miles when an estimated force of 10 or 11, which has 
been not unfrequently recorded during the colder months of the year, is 
reached and maintained for some time remains to be seen. Instances 
will in all probability occur during the autumn before the ice-deposits of 
the wind practically seal up the anemometer for the winter months. 

The mean temperature for the year ending May 1885 was 30°-G, or 
0°'3 below the calculated normal temperature given in last year's Report. 
The tempei'atures for the same period for stations in the more immediate 
neighbourhood were from 0°-3 to O''-^ below their normals, being thus 
identical with the deviation from the normal at the Observatory. The 
extremes of temperature for the year were GO°'l at 2 p.ji. August 9, and 
11°T at midnight and 1 A.M. February 16, thus giving a range of 49°-0. 
The coldest week yet experienced was the week ending February 21, the 
mean of which was lG''-2. In this week the lowest temperature for the 
year occurred, and the humidity fell to 22. Great dryness associated 
with great cold scarcely ever occurs in the weather records of the Ben, 
and in this case the exceptionally cold dry weather terminated with the 
great storm of the 21st and 22nd February already referred to. 

From the observations of the maximum and minimum thermometers 
the mean daily range of temperature is — in winter, 6°'8 ; spring, 6°'4 ; 
summer, 7°'l ; and autumn, 6°-6 — there being thus little variation with 
season. From the dry bulb, there is only 0°'7 between the mean coldest 
and mean warmest hour of the day in winter, but in summer the diffe- 
rence is 3°'0. It follows that in all seasons, but particularly in winter, 
the changes of temperature which occur are only in a subordinate degree 
due to the direct influence of the sun, but are chiefly caused by the 
passage of cyclones and anti-cyclones over the Observatory. Indeed, it 
may be regarded that, in the stormy months of winter, the Ben Nevis 
observations present the cyclonic and anti-cyclonic changes of tempera- 
ture in their simple conditions, uninfluenced by the heat of the sun. 

Lower relative humidities were observed than during the previous 
year. On January 20, the mean of the twenty-four hours gave the very 
low mean humidity of 32. On the 15th of the same month, at 5 a.m., the 
dry bulb was 20°-9 and the wet 16°-2, which from Glaisher's tables indi- 
cates a dew-point at — 16°-2 and a humidity of 19, being respectively the 
lowest yet noted on the top of Ben ISTevis. The lowest temperature ever 
observed anywhere in the British Islands was — 16°-0, at Springwood 
Park, near Kelso, in December, 1879, which closely agrees with the lowest 
dew-point on Ben Nevis. As regards atmospheric pressure, it is only in 
winter that the afternoon minimum falls below the mean daily pressure ; 
in summer this daily minimum is 0-007 inch above the daily mean. On 
the top of Ben Nevis, atmospheric pressure of the three seasons, spring, 



92 EEPORT — 1885. 

summer, and autumn, is above tlie daily mean for fifteen hours, from 10 A.M. 
to midnight, and below it for nine hours, from 1 to 9 A.M. In June, when 
the sun's heat is most powerful, the afternoon minimum is the least 
pronounced, and the diurnal curve of pressure tends towards a single 
maximum and minimum, similar to what occurs in the same months over 
the open sea in the higher latitudes. Except in mid-winter these seasonal 
peculiarities of the pressure are seen in the results of each month's obser- 
vations, and the regularity in the changes from month to month, in the 
times of occui-rence of the four phases of the pressure, is very striking. 

The sunshine-recorder shows 461' hours of suushine for the twelve 
months, which is about 11 per cent, of the possible sunshine. As regards 
the partition of the sunshine through the hours of the day, the most note- 
worthy circumstance is that daring spring, summer, and autumn the 
amount is very considerably greater before noon than after it. As com- 
pared with the afternoon, the sunshine of the forenoon is 43 per cent, 
greater in spring, 60 in summer, and 33 in autumn, whereas in winter the 
amounts are nearly equal. During summer the maximum sunshine occurs 
from G to 9 a.m. This diminution in suushine later in the day is no doubt 
caused by the ascending aerial currents which rise from the heated sides 
of the mountain during the warm hours of the day, and the condensation 
of the aqueous vapour into cloud which is the consequence. 

Very heavy rainfalls are of frequent occurrence on Ben Nevis. Of 
single hours the largest was 1'302 inch, from noon to 1 p.m. of December 
10, 1884. The largest daily fall was 4'264< inches, on December 10, 
1884, a fall all but equalled by that of October 25, which was 4-231 
inches. A fall of at least one inch occurs, on the average, one day in 
seven. Combining all the rainfall observations made since June, 1881, 
the following are the averages ; those from July to September being for 
four j^ears, June and October for three years, and November to May 
one year only. 

inches inches 

January . . . 7-33 May .... 837 
February . . 10-94 June. . . . 880 

March . . . 12-89 Juh .... 1070 
April . . . 485 August . . . 11-24 



inches 
September . . 944 
October . . 11-0& 
November . . 1930 
December . . 25-20 



Year, 146-14 inches. 



There can be little doubt that the Ben Nevis Observatory has the 
largest rainfall of any place in Scotland at which a rain-gauge has hitherto 
been observed. 

The observations at Fort William by Mr. Livingston, consisting of 
eye observations six times a day, and continuous recoi'ds of the atmo- 
spheric pressure and temperature by a barograph and thermograph, 
have been regularly carried on during the year. It is not possible to 
over-estimate the value of these sea-level observations at Fort William, in 
their relations to the observations made on the top of Ben Nevis, it being 
from these relations that the Ben Nevis observations have their supreme 
importance in discussing the great problem of the weather changes of 
North-western Europe. This inquiry is now being carried on under the 
superintendence of the Directors of the Observatory. 



ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 93 



Seventeenth Report of the Covimittee, consisting of Professor 
Everett, Professor Sir W. Thomson, INIr. Gr. J. Symoxs, Sir A. C. 
Kamsay, Dr. A. GtEIKIE, JMr. J. Gtlaisher, Mr. Pengelly, Pro- 
fessor Edward Hull, Professor Prestwich, Dr. C. Le Neve 
Foster, Professor A. S. Hersciiel, Professor Gr. A. Lebour, Mr. 
Galloway, ]Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. 
Wethered, and Mr. A. Strahan, appointed for the purpose of 
investigating the Rate of Increase of Underground Temperature 
dowmvards in various Localities of Dry Land and under 
Water. Drawn up by Professor Everett (Secretary). 

The present Report is for the two years wbicli have elapsed since the 
summer of 1883. 

Observations have been taken in a deep bore at Richmond, Surrey, 
by Mr. Collett Homersbam, M.Inst. C.E., F.G.S. It is on the premises of 
the Richmond Vestry Waterworks, on the right bank of the Thames, 
and about 33 yards from high- water mark. The surface is 17 feet above 
Ordnance datum. 

The upper part consists of a well 253 feet deep, with an internal 
diameter of 7 feet at top and 5 feet at bottom, which was sunk in 187G 
for the purpose of supplying water to the town of Richmond, and carried 
down to the chalk. From the bottom of the well a 24-inch bore-hole 
was sunk to the total depth of 434 feet, thus penetrating 181 feet into 
the chalk. This portion of the work was completed in 1877. Above 
the chalk were tertiaries, consisting of 160 feet of London clay, 60 feet 
of the Woolwich and Reading beds, and some underlying sands. TJie 
water yielded at this stage was about 160 gallons a minute, and when 
not depressed by pumping was able to rise 4 or 5 feet above the surface. 
Its ordinary level, owing to pumping, was about 130 feet lower. 

In 1881 the Richmond Vestry determined to carry the bore-hole to a 
much greater depth, and the deepening has been executed under the 
direction of Mr. Homersham's father, who is consulting- ensineer to the 
Vestry. 

The existing bore-hole was first enlarged and straightened, to enable 
a line of cast-iron pipes, with an internal diameter of 16^ inches, having 
the lower end driven water-tight into the chalic at a depth of 438 feet, 
to be carried up to the surface. The annular space surrounding this ])ipe 
served to furnish an uncontaminated supply of water to the town during 
the deepening. 

Tlie total thickness of the chalk was 671 feet. Below this was the 
upper greensand, 16 feet thick ; then the gault clay, 201^ feet thick ; 
then 10 feet of a sandy rock, and a thin layer of phosphatic nodules. 
Down to this point the new boring had yielded no water. Then followed 
a bed 87^ feet thick, consisting mainly of hard oolitic limestone. Two 
small springs of water were met with in this bed at the depths of 1,203 
and 1,210 feet, the yield at the surface being 1^ gallons a minute, with 
power to rise in a tube and overflow 49 feet above the ground. A partial 
analysis of this limestone rock showed it to contain 2-4 per cent, of 



94 REPORT — 1885. 

sulphide of iron in the form of pyrites. At the depth of 1,239 feet this 
limestone rock ended, and hard red sandstone was found, alternating 
with beds of variegated sandy marl or clay. After the depth of 1,253 
feet had been attained, the yield of water steadily increased as the boring 
was deepened, the overflow at the surface being 2 gallons a minute at 
1,254 feet, 8 gallons at 1,363 feet, and 11 gallons at 1,387 feet. It rose 
to the top of a tube carried 49 feet above the surface, and overflowed ; 
and a pi-essure-gauge showed that it had power to rise 126 feet above 
the surface. 

The diameter of the bore was 16|^ inches in the chalk, 13^ inches in 
the gault, llj inches in the oolitic limestone, and at the depth of 1,334 feet 
it was reduced to a little under 9 inches. At 1,337 feet the method of 
boring was changed, and instead of an annular arrangement of steel 
cutters, a rotary diamond rock-boring machine was employed. The bore- 
hole, with a diameter of 85 inches, was thus carried down to 1,367^ feet, 
at which depth, lining tubes having to be inserted, the diameter was re- 
duced to 7j inches, and this size was continued to 1,447 feet, at which 
depth the boring was stopped. 

The bore-hole was lined with strong iron tubes down to the depth of 
1,364 feet ; and those portions of the tubes that are in proximity to the 
depths where water was struck were drilled with holes to admit the 
water into them. Three observations of temperature were taken at the 
depth of 1,337 feet, during the interval between the removal of the steel 
borers and the erection of the diamond boring-machine. The bore-hole 
was full of water, which was overflowing at the rate of from three to four 
gallons a minute. The thermometer employed was an inverted Negretti 
maximum, supplied by the secretary-. In each case the temperature re- 
corded was 75^° F. In the first observation, March 25, 1884, the ther- 
mometer was left for an hour and a quarter at the bottom of the bore-hole, 
and three weeks had elapsed since the water was disturbed by boring. 
The second observation was taken on March 31, when the thermometer 
was 5i hours at the bottom. In the third observation special precau- 
tions were taken to prevent convection. The thermometer was fixed 
inside a wroiight-iron tube, 5 feet long, open at bottom. The thermo- 
meter was near the lower end of the tube, and was suspended from a 
water-tight wooden plug, tightly driven into the tube. There was a 
space of several inches between the plug and the thermometer, and this 
part of the tube was pierced with numerous holes to allow the escape of 
any cold water which might be carried down by the tube. The tube was 
one of a series of hollow boring- rods used in working the diamond drill- 
machine. By means of these it was lowered very slowly, to avoid dis- 
turbance of the water as much as possible ; and the tube containing the 
thermometer was gradually worked through the sand at the bottom of 
the bore-hole. The lowering occupied five hours, and was completed at 
noon on Saturday, June 7. 

Cement, mixed with sugar, for the purpose of slow setting, was imme- 
diately lowered on to the surface of the sand, and above this a mixture of 
cement and sand, making a total thickness of 3 or 4 feet of cement 
plugo-ing. The thermometer was left in its place for three full days, the 
operation of raising being commenced at noon of Tuesday, June 10, and 
completed at 5 p.m. The thermometer again registered 75^° F., exactly 
the same as in the two previous observations which were taken without 
plugging. It would therefore appear that the steady upflow of water in 



ON THE EATE OF INCEEASE OF UNDEEGEOUJJD TEMPEEATUEE. 95 

the lower part of the bore prevents any downward convection of colder 
water from above. 

The boring has since been carried to the depth of 1,447 feet, with a 
diameter reduced to 7^ inches, and Mr. Homersham made preparations 
for a final observation at the bottom with a plug consisting of a thick 
india-rubber disc covered with cement and saud ; but the vestry declined 
to incur the responsibility of having the rods lowered again for this 
purpose ; and as some pieces of broken lining-tube had fallen in, there 
would have been serious risk of jamming. Mr. Homersham accordingly 
contented himself with lowering the thermometer to the bottom without 
plugging. It remained down for six days (Febrnary 3 to 9, 1885), and 
gave a reading of 76^° F. The water overflowing at the surface had a 
tempei-ature of 59° F. 

To deduce the mean rate of increase downwards, we shall assume a 
surface temperature of 50°. This gives for the first 1,337 feet an increase 
of 251°, which is at the rate of 1° F. in 62-4 feet, and for the whole 
1,447 feet an increase of 26J°, which is at the rate of 1° F. in 54'1 feet. 
These results agree well with the Kentish Town well, where Mr. Symons 
found in 1,100 feet an average increase of 1° in 55 feet. 

]Mr. Homersham carried on a lengthened correspondence with the 
secretary as to the best manner of taking the observations, and the 
method devised by him as above described will famish a useful model for 
future observers. 

Thanks are also due to the Richmond Vestry for permission to 
observe, and to the contractors, Messrs. Docwra, for the loan of their 
apparatus. 

Mr. Galloway (member of the Committee) has furnished observations 
taken daring the sinking of a shaft to the depth of 1,272 feet in or near 
the Aberdare valley, Glamorganshire. The name of the place is Cwm- 
pennar, and the position of the shaft is on the slope on the east side 
of the valley, near the summit of the hill which separates it from the 
Merthyr valley. The mouth of the shaft is about 800 feet above sea 
level. 

Observations were taken at four different depths, 546 feet, 780 feet, 
1,020 feet, and 1,272 feet, the thermometer being in each case inserted, 
and left for twenty-four hours, in a hole bored to the depth of 30 inches, 
at a distance not exceeding 2-Jy yards from the bottom of the shaft for the 
time being. About eight hours elapsed between the completion of the 
hole and the insertion of the thermometer. The strata consist mainly 
of shales and sandstone, with a dip of 1 in 12, and the flow of water into 
the shaft was about 250 gallons per hour. 

The first of the four observations was taken in the fireclay under the 
Abergorkie vein ; the second in strong * clift ' (a local name for arena 
ceous shale) in disturbed ground ; the third in bastard fireclay under a 
small rider of coal previously unknown ; the fourth in ' cHft ' ground two 
yards above the red coal vein, which overlies the 9-foot seam at a height 
of from 9 to 12 yards. The observations were taken by the manager, 
Mr. John Beith, and are as follow : 



epth in ft. 
546 


Temp. Fahr 
56° 


780 
1,020 
1,272 


69j° 

63° 

66^° 



96 



REPORT — 1885. 



Comparing consecutive deptlis from 546 feet downwards, we liave the 
following increments of temperature : — 

3i° in 234 ft., giving 1° for 67 ft. 



3i° 

■sl° 



240 



69 



— showing a remarkably regular rate of increase. A comparison of the 
first and fourth observations gives an increase of 101° in 726 feet, which 
is at the rate of 1° F. in 691 feet. As the surface slopes about 1 in 5, and 
the pit is near the summit of a ridge, it is probable that in level ground 
of similar material the rate would be about 1° F. in 60 feet. 

As a check upon this result, we find that this rate of decrease reck- 
oned upwards from the smallest depth (546 feet) would give a surface 
temperature of (56 — 7-9 =) 48°-l, which, as the elevation is 800 feet, is 
probably very near the truth. 

Mr. Garside has sent an observation of temperature taken by himself 
in the roof of the Mersey tunnel in August 1883. The temperature was 
53°, the depth below Ordnance datnm being 92 feet. A great quantity 
of water from the river was percolating through the sides of the tunnel. 

On Auo-ust 13, 1884, he verified his previous observation in Denton 
Collieiy (Ibth Report). The second observation was made at the same 
depth as the first (1,317 feet), in the same pit and level, and under the 
same circumstances, except that the thermometer was allowed to remain 
fourteen days in the hole bored for it, instead of only six hours. The 
temperature observed was the same as before, namely 66°. 

Mr. Garside has also supplemented his previous contribution to our 
knowledge of the surface temperature of the ground in the East Man- 
chester coal-field (16th Report) by two more years' results from the 
same observing stations. The following are the collected results, includ- 
ing the year previously given : — 

Croft House, in the centre of AsJdmi-under-Ljjne, 345 ft. above sea. 



I 



— 4 ft. Deep 


1 ft. Deep 


Mean of Max. 
and Min. Air 


1882 
1883 
1884 


47°-5 
46° G 

4S°-3 


46°-2 
45°-o 
47°-3 


48°-4 
47°-8 
48°-9 


Means 


47°-5 


46°-3 


48°-4 



District Ivfirmary, 501 ft. above sea. 


— 


4 ft. Deep 


1 ft. Deep 


Mean of Max. 
and Min. Air 


1882 
1883 
1884 


45°-9 

46°-3 

470.7 


4.5°-6 
45°-3 
47° 3 


46°-6 
46°-3 

48°-2 


Means 


4€°-6 


46°1 


47°0 



Giving equal weight to the 4-foot and 1-foot observations, we have a 
mean surface temperature of 46°-9 at an elevation of 345 feet, and 46°-4 



ON THE EATK OF INCIIEASE OF 0x\DERGKODND TEMPEllATUUK. i>7 

at 501 feet. The diBFerence between them agrees well with the generally 
accepted rate of 1° for 300 feet, and indicates about 48° as the surface 
terapsrature at small elevations, such as 30 feet. The pits in the East 
Manchester coal-field from which we have observations, namely, Astley 
Pit (Uakinfield), Ashton Moss, Bredbury, Denton, and Nook Pit, are all 
sunk in ground at elevations of between 300 and 350 feet. It would 
therefore appear that the assumption of a surface temperature of 49°, 
which wc made in reducing these observations, is about 2° in excess of 
the truth. 

A very elaborate paper on Underground Temperature has recently 
been communicated to the Royal Society by one of the members of the 
Committee — Professor Prestwich. It contains probably the fullest col- 
lection that has ever been made of observations of underground tempera- 
ture, accompanied iu most cases by critical remarks ; and adduces 
arguments to show that most of the temperatures observed are too low, 
■owing to the influence of the air in mines, and of convection currents in 
wells. Professor Prestwich is disposed to adopt 1° F. in 4-3 feet as the 
most probable value of the normal gradient. 



Report on Electrical Theories. 
By Professor J. J. Thomson, M.A., F.R.S. 

In this report I have confined myself exclusively to the considei-ation of 
those theories of electrical action which only profess to give mathematical 
■expressions for the forces exerted by a system of currents, and which 
make no attempt to give any physical explanation of these forces ; for it 
is evident that before we can test any theory of electrical action we mu.st 
know what the actions are \vhich it has to explain, and we cannot do this 
until we have a satisfactory mathematical theory. 1 have further limited 
myself to the consideration of the fundamental assumptions of each 
theory, and have not attempted to give any account of its mathematical 
developments, except in so far as they lead to results capable of distin- 
guishing between the various theories. 

I have divided the theories into the following classes : — 

1. Theories in which the action between elements of current is deduced 
by geometrical considerations combined with assumptions which are 
not explicitly, at any rate, founded on the principle of the Couservatioii 
of Energy. 

This class includes the theoi'ies of Ampere, Grassmann, Stefan, and 
Kortewee. 

2. Theories which explain the action of currents by assuming that 
the forces between electrified bodies depend upon the velocities and accele- 
rations of the bodies. 

This class includes the theories of Gauss, Weber, Riemann, and 
Clausius. 

3. Theories which are based upon dynamical considerations, but which 
neglect the action of the dielectric. 

This class contains F. E. Neumann's potential theory and v. 
-Helmholtz's extension of it. 

4. C. Neumann's theory. 

1.88.5. H 



98 REPOET — 1885. 

5. Theories which are based upon dynamical considerations, and which; 
take into account the action of the dielectric. 

This class includes the theories of Maxwell and v. Helmholtz. 

We shall now proceed to the detailed consideration of these theories. 

Theories in which the action between elements of current is deduced hy 
geometrical considerations combined with certain assumptions which 
are not e.rplicitly, at any rate, foutuled on the Principle of the Conser- 
vation of Energy. 

The best known theory of this class is that of Ampere. Others, 
however, have been given by Grassmann, Stefan, and Korteweg, which 
we shall consider in order. 

Am,pere's Theory. 

This theory was first published in 1820. In 1823 appeared his great 
paper, the ' Memoire sur la Theorie Mathematique des Phenomenes 
Electro-dynaraiques,' Memoires de VInstitut, t. vi., which Maxwell de- 
scribes as ' perfect in form and unassailable in accuracy,' and which at 
once brought the action between electric currents under the power of 
mathematics. Ampere founded his theory on certain postulates which 
he attempted to establish by experiment ; inasmuch, however, as he 
always dealt with closed circuits in his experiments and elements of 
circuit in his postulates, the experimental evidence is not quite satis- 
factory. Ampere's experiments have been repeated by v. Ettingshausen ^ 
with much more delicate apparatus. 

The postulates used by Ampere are as follows. The first four are 
given in the words of Professor Tait : — ^ 

I. ' Equal and opjoosite currents in the same conductor produce equal 
and opposite effects on other conductors ; whence it follows that an 
element of one current has no effect on an element of another which lies 
in the plane bisecting the former at right angles.' 

II. ' The effect of a conductor bent or twisted in any manner is 
equivalent to that of a straight one, provided that the two are traversed 
by equal currents and the former nearly coincides with the latter.' 

III. ' No closed circuit can set in motion an element of a circular 
conductor about an axis through the centi-e of the circle and perpendicular 
to its plane.' 

lY. ' In similar systems traversed by equal currents the forces are 
equal.' 

Y. ' The action between two elements of current is a force along the 
straight line joining them, and proportional to the product of the lengths 
of the elements and the currents flowino' through them.' 

It follows from IV. that the force between two elements of current 
varies inversely as the square of the distance between them. 

The assumption Y. is one that can only be justified by the correctness 
of the results to which it leads. We have no right to assume i^t priori 
that the action is equivalent to a single force, and not to a force and a 
couple : and we have no more right to assume that the force is along the 
line joining the elements than we have to assume that the force between 

' ' Ueber Ampere's elektrodynamische Funclamentalversuche,' Wicn. Ber, (11), 77,. 
p. 109, 1878. 

- Tait's Quaternion?, 2nd edit. p. 249. 



ON ELECTRICAL THEORIES. 99 

two small magnets is along the line joining their centres, and in this case 
the assumption is untrue. It is in the nature of the assumption V. that 
Ampere's theory differs from others of this class. The second part of 
T. depends upon V. It is not true unless we assume that the force 
between two elements is along the line joining them. 

Ampere deduces the force between two elements of current from these 
principles in the following way : — Suppose we have two elements of current 
of lengths dsi, ds^ traversed by cui-rents of strengths i, j respectively. 
Let us take the line joining the centres of these currents as the axis of x ; 
let the plane of c?s, and x be taken as the plane of xy ; let 0,, 6^ be the 
angles which cZs,, ds^ respectively make with the axis of x, rj the angle 
which the plane through tZs., and ;• makes with the plane of xy. 

By Ampere's second pi'oposition the action of ds^ on ds.2 will be the 
sum of the action of 

f fZ^i cos d^ or a, along x 
\ d'*i sin ^1 or /3i along y 
on 



ds^ cos 02 01* "2 along x 

ds2 sin 02 t'os V or ft^ along y 

ds2 sin 02 sin ?/ or yg along z. 



Now by proposition I. «[ cannot exert a force on either /Sg or 72* 
because it is in planes which bisect /j, and y.y at right angles, so that the 
only component on which a-^ can exert a force is u^. Let the force between 
these components be 

a 

-2-«l«2- 

■where r is the distance between the centres of the elementary currents. 

In the same way we can show that the only component on which /3, 
can exert any force is jo.2- I^^t the force between these two elements be 

^ ,•> a 
r- 

Thus the force between the two elements ds^, ds^ is 

— (aai«2 + 6/3 1/3 2}, 

or, substituting for a^a^, r'lft-z their values : 

-J [a cos 0, cos 9-2 + h sin 0i sin 09 cos tj} ij f?Si cZsg. 

The proposition III., that the action of a closed circuit on an element of 
current is always at right angles to the element, leads on integration to 
the condition 

2a + i = 0, 

so that the force between the two elements equals 

-jj {cos 01 cos 02 — 2 sin 6^ sin 00 cos t]] ijdsy ds^. 

IFrom this we ai'e able to find the force between any two circuits or parts 
of circuits- To find the force on a magnetic system, Ampere used his 

H 2 



100 EEPORT— 1885. 

principle that the magnetic action of an electric current was the same as 
that due to a magnetic shell bounded by the circuit and magnetised to 
the proper intensity. In this way Ampere gave a complete theory of the 
action of currents upon currents and upon magnets — in fact, a complete 
theory of all the effects produced by a current which were known when 
his paper was published. 

It is difficult to overrate the service which Ampere's theory has 
rendered to the science of electrodynamics. Perhaps the best evidence 
of its value for practical purposes is the extreme difficulty of finding any 
experiment which proves that it is insufficient. In spite of this, how- 
ever, as a dynamical theory it is very unsatisfactory. If, as we are led 
to do by Ampere, we attach physical importance to elements of current, 
and regard them as something more than mathematical helps for calcu- 
lating the force between two closed circuits, then we are driven to ask, 
not only what is the law of force between the elements, but what is the 
energy possessed by a system consisting of two such elements. If we do 
this, and find this energy by calculating the amount of work required to 
pull the elements an infinite distance apart, we arrive at the conclusion 
that the energy must depend upon the angles which the elements make 
with each other and with the line joining them ; but if this is so, then 
the force between the elements cannot be along the line joining them, 
and there must in addition to this force be couples acting on the elements. 
For these reasons we see that Ampere's theory cannot give the complete 
action between two elements of current. What it does — and this for 
practical purposes is an advantage and not a disadvantage — is to give 
in most cases, instead of the complete action between two elements, that 
part of it which really affects the case under consideration. 

Before discussing cases, however, in which the terms which Ampei-e 
neglects might be expected to produce measurable effects, we shall, in 
order to compare the various theories more easily, proceed to consider 
other theories of the same class. 

Grassmann's Theory.^ 

The method by which Grassraann obtains his theory is very remark- 
able. He objects to Ampere's formula for the force between two elements 
of current, because it makes the force between two parallel elements 
change from an attraction to a repulsion when the angle which the ele- 
ments make with theline joining them passes through the value cos~' 2/3, 
and the object of his investigation is to get a law of foi^ce free from this 
peculiarity, and which, while giving the same result as Ampere's for closed 
circuits, shall yet be as simple as possible. He begins by regarding any 
circuit as bailt up of ' Winkelstrome,' i.e., currents flowing along the two 
infinite lines which form any angle. He points out that a circuit of any 
shape can be built up of such currents ; the circuit ahc, for example, 
may be regarded as built up of the ' Winkelstrome ' eaf, fbg, and gee. 

Grassmann proceeds to calculate by Ampere's formula the action of 
a ' Winkelstrom ' upon an element of current («). Since the 'Winkel- 
strom ' will have no action upon an element of current perpendicular to 
its plane, we see that it is only necessary to calculate its action upon the 
component (a') of a in its own plane. Grassmann does this by calcu- 
lating the effect due to each arm of the ' Winkelstrom ' separately. He 

' Fogg. Ann. O-l, p 1, 1815 ; Crelle, 83, p. 57 



ON ELECTIUCAL THEORIES. 



101 



finds expression for the forces along and perpendicular to a', due to an 
infinite rectilinear current starting from a definite point. The force of 
such a current along a' does not depend on the angle the current makes 
with the line from its end to o', so that the effects of two such currents 
starting from the same point and flowing in opposite directions, i.e. of a 
' Winkelstrom,' will be to produce no force along o' ; thus the effect of a 
' Winkelstrom ' on an element of current in its own plane will be a force 
at right angles to the element. The force at right angles to a' due to a 
rectilinear current will consist of two parts, one independent of the angle 
made by the current with the line joining its end to the element, the 
other depending upon this angle. The first part will vanish when we 
consider a ' Winkelstrom ' ; the second part only will produce any effect. 




Now Grassmann says that it will much simplify the analysis, and obviously 
(since any closed circuit may be built up of 'Winkelstrome ') lead, for 
closed circuits, to the same result as Ampere's formula, if we suppose that 
the law of force between elements of currents is such that the only effects 
produced by a rectilinear current are those which do not vanish for a 
' Winkelstrom,' and hence that a straight current exerts on an element of 
current a force at right angles to the projection of the element on the 
plane containing the centre of the element and the rectilinear current, 
and that the magnitude of this force is 



ij ds' 



cot 



2' 



where i is the sti*ength of the rectilinear cnnent, y the strength of the 



102 KEPORT — 1885. 

element of current, ds' its projection on the plane through its centre 
containing the straight current, r the distance of the element from the 
end of the straight current, and o the angle which the rectihnear 
current makes with the line joining its extremity to the elementary- 
current. By taking the difference of two such rectilinear currents, 
Grassmann finds the action of an element (/3) of current on another 
element («) is a force at right angles to a', the component of a in the 
plane containing /3 and the middle point of a and equal to 

. . dads' ■ n 
^3 -72- «^^ ^' 

where is the angle which /3 makes with r, da the length of (/3), and j the 
current flowing through it. 

The direction of the force is along AB, where A is the centre of the 
element (a) and B the point where the normal to a' is cut by /3 produced 
in the direction of the current. 

If we treat this theory in the same way as we did Ampere's on p. 
99 by considering the action of the component a,, /3i of an element of 
current ds, on the components 02, /^o, 72 of another element ds.,, we see 
that Grassmann's theory is equivalent to supposing that a, exerts no 
force on a^, ft.^, or 72 ; i^l^at ft^ exerts a force A/JjUo on u^ at right 
angles to a.^ in the plane of xxj, and a force A/3i/32 on /32 at right angles 
to it, that is, along the line joining the element, and that it exerts no 

force on y^- .... 

Thus we see that Grassmann's theory :s equivalent to replacmg 
Ampere's assumption, that the force between two elements of current 
acts along the Hue joining them, by the assumption that two elements of 
current in the same straight line exert no force on each other. 

As a dynamical theory of electrodynamics, Grassmann's theory is open 
to the same objection as Ampere's, that it does not take into account the 
couples which may exist between the elements, and also to the additional 
objection that, according to it, the action of an element of current ds^ on 
another element ds.^ is not equal and opposite to the action of ds^ on 
dsi, so that the momentum of the two elements cZs, and ds.^ will not 
remain constant, and, as the theory does not take into account the sur- 
rounding ether, there is no way of explaining what has become of the 
momentum lost or gained by the elements. As a piece of geometrical 
analysis, however, the theory is very elegant and worthy of the author of 
the ' Ausdehnungslehre.' 

From the way in which Grassmann's theory was developed we see 
that between closed circuits it must give the same forces as Ampere's ; for 
unclosed circuits this is not the case, and Grassmann, at the end of the 
paper quoted above, mentions a case where the two theories would give 
opposite results, assuming that unclosed streams exist. Suppose we have 
a magnet //s and an unclosed current AB in the same plane as the 
magnet and passing through its middle point, then if Ampere's theory 
be true, the magnet will twist in one direction ; if Grassmann's, it will twist 
in the opposite. This depends upon the change, according to Ampere's 
theory, of the force between two parallel elements from attraction to repul- 
sion, when they make the angle with the line joining them at less than 
sin-' 1 / v/'3', while according to Grassmann's theory, there is no such 
change. 



ON ELECTRICAL THEORIES. 103 

Stefan's Theory} 

This resembles Ampere's theory very closely, except that Stefan does 
•not make the assumption that the force between two elements of current 
is along the line joining them : this difference leads to the introduction 
of two forces which Ampere neglects. 

We shall use the same notation as when we discussed Ampere's 
theory, and consider, as before, the action of an element of current dsi 
on another element dso. Stefan, like Ampere, assumes that we may 
replace an element of current by its component, so that we have to con- 
sider the action of the components («,, /^i) of ds^ on the components 
(«2) ^21 y-i) of c7S|. 

As in Ampere's theory, the component a, is supposed to exert a force 



r2 



on a 2, this force by symmetry must be along the line joining the 
elements. 

a, is supposed to exert a force on ji^ equal to 

along the axis of y. We can see that this force may exist, for it is 
conceivable that it should be in the same direction as jl.2 when a, points 
from the middle of ds^ to the middle of ds<i, and in the opposite direction 
to 1^2 when ctj points in the opposite direction. Stefan assumes that a^ 
exerts no force on /32 parallel to the axis of z, and no force at all on 72- 

/jj is supposed to exert a force on uo parallel to the axis of y and 
equal to 

d -, 
r- 

We may see, by the same reasoning as we used before for the force 
between /J, and «2> that it is conceivable that this force may exist. /3i is 
supposed to exert no force on 05 parallel to the axis of z. 

As in Ampere's theory, /ji is supposed to exert a force on j32 equal to 

^ . -, 

-^Pilh, 

this force must by symmetry be along the line joining the elements ; /3, 
is supposed to exert no force on 72- 

Thus the action of ds^ on dsg consists of a force 

72 |ani«2+ ^Pi/32 j 
.along the line joining the elements, and a force 

72 |c«i,'32 + cZ/3i"2| 

at right angles to this line in the plane containing dsi and r. If we take 
' Stefan, Wien. Sitzungshcriclde, 59, p. 693, 1SG9. 



104 



REPOllT 1885. 



arbitrary coordinate axes and suppose that .v, y, z are the coordinates of cZs,^ 
a;', 2/', z' those of ds.,, then the x component of the force on ds2 due to dn^ 



is shown by Stefan to be equal to 
d 



'■-^''^''^^'M^^^rjr 



(a;' — x) d 1 dx^ d 

r dni r ds.2 ^ 



__ 1 dx 
dso r da. 



3=1-^ 



+ 2- 



cost 



■with similar expressions for the force parallel to the axes of y and z. 



Here /, j are the currents through 
between the elements of current, and 



')n:= 



3 l" 



•C- 



ds2 respectively, £ is the angle- 

n=l{a-h-c + 2d} 
f= —^{ii — h + 2c-d] 
q=^[a + 2h-c-d]. 

We see from this expression for the force parallel to x that the last 
term is the only one which does not vanish when integrated round two- 
closed circuits of which ds, and ds^ are elements. So that the force will 
depend only upon // ; the value of q will depend upon the units we adopt : 
in Stefan's work q is put equal to —1/2. 

This is the only condition to be got by considering the translatory 
foi'ce between two circuits ; we can get another by considering the couple 
acting on the closed circuit, supposed rigid, of which ds^ forms a part. 
For the s component N of this couple Stefan finds the expression 

c7ii'' dy _dy^ dx 



N 



= U2fP 



y^x — x^y 



cos £ dsids2 — 1 



JP 



'fir c7ii'' dy _dy^ ^•'' 1 i 
J r \ ds^ ds^ ds2 ds^ J 



c?>-,. 



But supposing the two circuits to have a potential 



U 



cos £ 



p: 



ds■^ ds.,, 



we can easily see that the couple 

. . rr.'/'.v-.'y'y 

= IJ ;3 - cos £ dSidS.2 



n 



'llL _ ^'^\ 7 , 

c/s, ds, dsa ds, ' ' 1 ■ '-^ 



'2 



1 



i 



thus if two circuits have a potentij 



or substituting fovp and q their values, 

2a + b + C-2d^0. 
If c=0 and (.7=0, as in Ampere's theory, this relation becomes 

2a + b = 0, 

which is the same relation as Ampere deduced by finding the condition 
that the foi'ce due to a closed circuit on an element of current should be 
at right angles to the element, and Stefan has proved that on his theory 
the same condition leads to the equation 

p = q, 

i.e., the same condition as the one which expresses that two closed circuits 
have a potential. 



ON ELECTRICAL THEOUIES. 105 

Stefan shows that, fi'om the consideration of the action of closetT. 
circuits on elements of other circuits or of themselves, it is impossible to 
get any other relation between the quantities a, b, c, d, so that we have 
only two relations between the quantities a, h, c, d, and thus two of them 
must be indeterminate. 

We may give any values we please to these quantities, provided the}- 
satisfy these two relations ; if we put c = 0, c? = we get Ampere's theory ; 
if or, ^ 0, c = 0, Grassmann's ; and we can get a number of other theories by 
giving different values to these quantities. 

Stefan's theory is open to the same objection as Ampere's, since it 
does not take into account the couples which one element may produce 
on another. He also limits the generality of his theory by supposing that 
the force between two elements of currents in one plane is in that plane. 

Korteicey's Theory.^ 

According to this theory, the forces between two elements of current 
are the same as in Stefan's theory ; Korteweg, however, considers in 
addition the couples which one element may produce on another. 

If we use the notation we adopted in discussing Stefan's theory, we 
have, considering the force on dso, a force 

along the line joining the elements, and a force 

parallel to the axis of y. 

In addition. to these forces, Korteweg supposes that from the action of 
«! on /Bj there is a couple whose axis is parallel to the axis of z equal to 

and from the action of «i on y^ a couple on yg whose axis is parallel to 
the axis of y and equal to 

-/ar/2; 

from the action of /Jj on a 2 there is a couple on a. 2 whose axis is parallel 
to the axis of '4 and equal to 

and from the action of /^i on y^ there is a couple on y., whose axis is 
parallel to the line joining the elements and equal to 

A/3,02. 

If we now take arbitrary co-ordinate axes, the forces on the element d,--, 
are the same as those given by Stefan's theory. The couples, however, are 
different. The component parallel to the axis of x of the couple 011 
ds2 is given by the equal iuti 

_r2 d,2 \ ./.-, cL-^J r* ds2 ds ^'' "^^ 

' Crelle, xc. p. 49, 1881. 



lOH EEPORT — 1885. 

(h + a) dr / , , s dz, , , . dij'^ \ 
r dsi L (li<2 "*2 J 

7 / f'//' ''■s dy dz "1 ~| 

I (Is 2 dsi dni ds2 J J 



ii dsi ds2, 

with similar expressions for the components of couple around the axes of 
y and z. 

By making the force between two closed circuits have the same value 
as that given by Ampere's theory, Korteweg finds that 

a + 2b-d-c = - 3A2, 

where A is a constant quantity whose value depends upon the unit of 
current adopted. 

By making the couples produced by one closed circuit on another 
have the same value as that given by Ampere and the potential theory, 
he finds that 

i ('•''^0 + (iZ-^O r-c + 2A2 = 0. 
dr 

Korteweg considers that the experiments of v. Ettingshausen, quoted 
above, prove (1) that the force on an element of circuit produced by a 
closed circuit is at right angles to the element, and (2) that the couple on 
an element due to a closed circuit has the value given by Ampei'e's theory. 
The first condition gives 

c-h = 2A2; 
the second the two conditions 

h + g = 0. 

And he points out that we cannot get any more conditions by consi- 
dering the action between two closed circuits, or the action of a closed 
circuit on an element of another. 

It should be noticed that since, according to this theory, part of the 
action of one element of a circuit on another consists of a couple, the 
condition that the force due to a closed circuit on an element of another 
should be at right angles to the element is not, as in Stefan's theorj', iden- 
tical with the condition that the expression for the couple exerted by one 
closed circuit on another should be the same as that given by Ampere. 

This theory is valuable because it is the most general one of the class 
we are considering which has been published. It is the only one which 
takes into account the couples, and by giving special values to the quan- 
tities a, h, c, d,f, g, h, we can get any of the other theories of this class. 



ON ELECTRICAL TIIEOinES. 107 

■On the theories which explain the action of currents hij assuming that the 
forces beticeen two electrified bodies depend upon the velocities and ac- 
celerations of the bodies. 

According to these theories a body conveying an electric current con- 
tains equal quantities of positive and negative electricity, so that it will 
Dot exei't any ordinary electrostatic eifect : the positive electricity is sup- 
posed, however, to be moving differently from the negative. In some of 
the theories (Weber's, Gauss's, Riemann's) Fechner's hypothesis, that the 
electric current consists of positive electricity moving in one direction 
(the direction of the current), and an equal quantity of negative elec- 
tricity moving at the same speed in the opposite direction, is assumed ; 
in other theories (Clausius') only one of the electricities is supposed to 
move, the other remains at rest. We can see in a general way how the 
assumption that the forces between two electrified particles depend on 
the velocities and the accelerations of the particles can explain the effects 
produced by an electric current. 

Let us take first the mechanical action between two circuits A and B, 
and let us consider the action of an element (a) of A on an element (6) 
of B. We shall consider first the action of the two electricities which are 
flowing through a on the positive electricity which is flowing through b. 
Since the motion of the positive electricity in a relative to that of the 
positive electricity in b is not the same as the motion of the negative 
electricity in a relative to that of the positive in b, the forces due to the 
positive and negative electricities in a will not counterbalance, so that 
there will be a resultant force on the positive electricity in b depending 
on the inequality between the motion of the positive and negative 
electricities in a relative to that of the jjositive in b. Similarly there 
will be a force on the negative electricity in b depending on the in- 
equality between the velocities of the positive and negative electricities 
in a relative to that of the negative in b, and, except for special laws of 
force and special values of the velocities of the electricities in b, this force 
will not be equal and opposite to the force on the positive electi-icity in b, 
so that a mechanical force on b will be produced by the currents through a. 

Let us now consider how inductive forces can be explained by this 
hypothesis : let us suppose that the element a is moving, and that the 
element b is at rest. The velocity of the electricity in a will be the 
resultant of the velocity with which the electricity flows through a and 
the velocity of translation of a itself, so that since the velocities of flow 
•of the positive and negative electricities are different, the actual velocity 
of the positive electricity will differ in magnitude from the velocity of 
the negative (unless, assuming Fechner's hypothesis, the element a is 
moving at right angles to itself) ; thus the force due to the positive 
electricity in a on a unit of positive electricity at b will not be equal and 
opposite to that due to the negative electricity in a, and thus there will 
be an E.M.F. at b due to the motion of a. This explains induction due to 
the motion of the primary circuit. 

Let us now consider induction due to the variation of the intensity of 
the current in the primary circuit. According to all the theories there 
IS a force produced by a moving electrified body proportional to the first 
power of the acceleration of that body. Let us consider the elements a 
and b again, and suppose that a variable current is flowing through a and 
BO current through b ; then if we suppose that a variation in the intensity 



108 KEi'oia — 1885. 

of a current is accompanied bj an alteration in the velocity of flow^ 
the acceleration of the positive electricity will, if we take Fechner's 
hypothesis, be equal and opposite to that of the negative ; but since there 
is a part of the force due to the moving electrified body which changes 
sign both with the electrification and the acceleration, the force due to 
the acceleration of the positive electricity will be equal in all respects 
to that due to the acceleration of the negative, so that there will be a 
resultant force on a unit of positive electtiuity at h, and this foi'ce is the 
electromotive intensity at b due to the alteration of the intensitj^ of the 
current in a. In this way we can explain the induction due to the varia- 
tion of the current in the primary circuit. 

Theories of this kind have been given by Gauss, Weber, Riemanu, 
and Clausius, and these writers have given expressions for the force 
between two electrified particles moving in any way. We shall after- 
wards consider these expressions in detail, but we may remark in passing 
that the theories of Gauss, Weber, and Riemann have much in common ; 
among other things they all lead to impossible results. In addition 
Clausius has shown that, unless we make Fechner's hypothesis about a 
current, viz. that it consists of equal quantities of positive and negative 
electricity moving with equal speeds in opposite directions, a current would 
on these theories exert a force on an electrified body at rest. 

The question of the forces due to moving electrified bodies is 
interesting in connection with electrolysis. Taking the ordinary view 
that the current is carried by the ions, we know from Hittorf 's researches 
that the anion and the cation move at different rates, so that the forces 
produced by these will be different ; hence we should expect an electrolyte 
conveying a current to exert a force on a charged particle at rest. 

We shall now go on to consider the various theories separately. 

Gauss's Theory.^ 

Gauss assumes that the force between two particles separated by a 
distance r and charged with quantities of electricity e and e' is along the 
line joining the particles and equal to 

where ii is the relative velocity of the two particles and c is a constant. 
This law will, if we make Fechner's hypothesis, explain the mecbanical 
force between two circuits ; but, since it contains no term depending on 
the acceleration, it cannot explain the E.M.F. produced by the variation 
of the strength of the current in the primary ; it is also inconsistent with 
the principle of the Conservation of Energy, and so we need not consider 
it any further. 

W. E. Weler's Theory.^ 

Weber assumes that the force between two charged particles, usiug 
the same notation as before, is 



ee 
r 



^{^-M'S-K;:fr)} 



' Gauss's theory was published after his death in his collected works, Gottingen 
edition, vol. v. p. 616. See also Maxwell's Electriclfi/ uivl Maijncthiit, 2ud edit, vol, 
ii. p. 440. 

- Weber's theory was published in 1846 in Abhundluwjeii der Kdmglich-Sdch-^ 



ON ELECTRICAL THEORIES, 109 

This fonnnla is not inconsistent witli the principle of tlie Consei'vation of 
Energy ; making Fechner's hypothesis, it will explain the mechanical force 
between circnits conveying currents ; it will also exjilain induction due 
both to the motion of the primary and the alteration in the strength of the 
current in the primary. We shall see, however, that it makes a body 
under certain circumstances behave as if its mass were negative ; i.e. if it 
were acted on by a force in a direction opposite to that in which it is 
moving, its velocity would continually increase. 

Riemann'.s Theory. 

This is explained in his ' Schwere Electricitat uud Magnetismus,' 
edited by Hallendorff, p. 327. According to this theory the force be- 
tween two electrified bodies is not altogether along the line joining them, 
but consists of the following parts : — 

1. A force along the line joining the particles equal with the same 
notation as before to 



?'{i-'l} 



2. A force on the first particle parallel to its velocity relative to the 
second equal to 

2ee' dr 



oh^'^di- 



3. A force on the first particle parallel to its acceleration relative to 
the second equal to 

-f, 



c'r 



where /is the relative acceleration of the particles. 

There are of course similar forces acting on the second particles, and 
we see from the form of the expressions of the forces that the force on the 
first particle is equal and opposite to the force on the second. Riemann's 
law of force is not inconsistent with the principle of the conservation of 
energy, and it explains the mechanical force between two circuits ; hence 
it must explain the induction of currents. We shall see, however, that it 
is open to the same objection as Weber's theory, viz. that it makes an 
electrified particle under certain circumstances behave as if its mass were 
negative. 

Glausius' Theory.^ 

If X, y, z are the co-ordinates of the first electrified particle, x' , y', z' 
those of the second, then according to this theory the x component of the 
force on the first particle is equal to 

— ee'x — < (J —vv cos i c^)~ > — -r -( - — 1 
[dxX^ ' \l c^ dt\r dtj] 

With similar expressions for the components parallel to y and z, here 

jslschen Gesellscluift der WissenscMften, 18ifi, p. 211 ; it is reprinted in Electro- 
dynamische Maassbestimmnnijen, 1871. A good account of the theory is given in 
Maxwell's Electricity and Maynetimn, 2nd edit. vol. ii. chap, xxiii. 

' This theory is given in Crelle, vol. 82, p. 85. There is also a fuU abstract in 
"Wiedemann's Beibldtter, vol. i. p. 143. 



to 



110 BEPOET — 1885. 

V and v' are the velocities of the first and second particles respectively, 
and E is the angle between their directions of motion. We may analyse 
these forces a little differently, and say that the force on the first particle 
consists of — 

1. A force along the line joining the pai'ticles equal to 

ee' f , , ; 1 

-2- s J —vv cosejv- > 

2. A force parallel to the velocity of the second particle and equal 

ec' <h- , 

3. A force parallel to the acceleration of the second particle equal 

to 

ee' dv' 

~'d^- 'df' 

We have, of course, corresponding expressions for the force on the second 
particle. 

Clausius' formulae differ from those of Gauss, Weber, and Riemann 
in two very important respects. 

1. They mike the forces between two electrified bodies depend on the 
absolute velocities and accelerations of the bodies, while the others make 
them depend only on the relative velocities and accelerations. 

2. They do not make the forces between the bodies equal and oppo- 
site, so that the momentum of the system does not remain constant. 

These results show that if this theory is ti'ue, we must take the ether 
surrounding the bodies into account. The first result can then be 
explained by supposing that the velocities which enter into the formulis- 
are the velocities of the bodies relatively to the ether at a considerable 
distance from the bodies, and the second result by supposing that the 
ether possesses a finite density, and that the momentum lost or gained by 
the bodies is added to or taken from the surrounding ether. 

The case is analogous to the case of two spheres A and B moving in 
an incompressible fluid ; in this case the forces on the sphere A depend 
on the velocities and accelerations of B relatively to the fluid at a great 
distance from the sphere, and ai-e independent of the velocity and accele- 
ration of A ; the forces are not equal and opposite, and the momentum 
lost or gained by the system is added to or taken from the momentum of 
the fluid. At the end of this section we shall see that, if we assume that 
variations in what Maxwell calls the electric displacement produce effects 
analogous to those produced by oi-dinary conduction currents, we get 
the same forces between moving electrified bodies as are given by Clausius' 
theory. 

Clausius' theory is not inconsistent with the principle of the con- 
servation of energy, and we shall see that it does not lead to the same 
diSiculty as the theoi'ies of Weber and Riemann, viz., that under special 
circumstances a body would behave as if its mass were negative. 

Assumino- that in an electric current we have equal quantities of 
positive and negative electricity moving with different velocities, Clausius 
has shown in the paper already cited that his theory gives Ampere's 
results for the mechanical force between two circuits, and the usual 



ON ELECTKICAL THEORIES. Ill 

expression for the induction due to tlie motion of the primary circuit, or 
variation in the strength of the current passing through it. 

Frohlich ' urges against Clausius' law that since, according to it, an 
electric current in motion exerts an electromotive force on a moving 
electrified particle, even though the particle is moving at the same rate 
as the circuit, every current on the earth's surface ought to exert an 
electromotive force on an electrified particle relatively at rest, since each 
is moving with the velocity of the earth. This force is one that can 
be derived from a potential, so that the integral of the force taken round 
a closed curve would vanish, and thus, even if this result were true, two 
circuits would not induce currents in each other if they were relatively 
at rest. Budde- points out, however, that the moving circuit would exert 
an electromotive force at each point of itself, and thus cause a separation 
of the electricity in the circuit, so that it would get coated with a distri- 
bution of electricity, the electrostatic action of which would balance that 
due to the action due to its motion on a point relatively at i^est. The 
velocities which enter into Clausius' formulje are velocities relative to the 
ether, so that if the ether moves with the earth, an electric current will, 
according even to this theory, exert no electromotive force on a point 
relatively at rest, and there will be no electrification on the surface of 
the circuit. The velocity c which occurs in all these theories is a velocity 
comparable with the velocity of light. 

General Considerations on these Theories.^ 

We shall now go on to discuss a general way of treating theories of 
the kind we have been considering. Perhaps the best way of doing this 
is to consider not the forces between the electrified bodies, but the energy 
possessed by them. If the energy depends on the electrification there 
will be forces between two electrified bodies. Now the potential energy 
depends on the electrification, and this dependence produces the ordinary 
electrostatic forces between two electrified bodies at rest. If, however, 
the kinetic energy as well as the potential depends on tlie electrification, 
then the forces between two electrified bodies in motion will be different 
from the forces between the same bodies at rest. An easy way of seeing 
this is by means of Lagrange's equations. 

If T be the kinetic energy, and x a co-ordinate of any kind, then we 
have, by Lagrange's equations, 

— — — = external force of type x. 
dt dx dx 

Hence if we have any term T' in the expression for the kinetic energy,, 
■we may, if we like, regard it as producing a force equal to 

_ ^J^' + ^ 
dt dx dx 

A simple illustration of this is afforded by the centrifugal force. In 

» Frohlich, Wied. Ann., ix. p. 277, 1880. 

* Wied. Ann., s. p. 553, 1880. 

' See Clausius ' On the Employment of the Electrodj-namic Potential for the 
Deterrnination of the Ponderomotive and Electromotive Forces,' I'kil. Mag., 1880, v. 
10, p. 255. 



112 REPORT— 1885. 

the expression for the kinetic energy of a moving particle there is the 
term 



■where r is tHe distance of the pai'ticle ivo'.n some fixed point, and d the 
angle which the i^adius from this point to the particle makes with some 
fixed line ; m is the mass of the particle. This terra, by the above rale, 
will give rise to a force of type r, i.e., along the radius vector equal to 

and this is the ordinary centrifugal force. 

Now let us consider a moving electrified body. If it is symmetrical, 
■and moves in an isotropic dielectric, it is evident that the electrification, 
if it enters at all, can only enter as a factor of the total velocity y, 
and cannot affect the separate components of the velocity differently. 

Let us suppose that the body is charged with a quantity of electricity 
denoted by e, then the kinetic energy, if it depends on the electrification, 
.must be of the form 

•where /(e) denotes some function of e. Now /(e) must be always 
positive, for if it were negative we could make 

\m + f{e) 

negative, and then the electrified body would behave like one of negative 
mass. The simplest form satisfying this condition which we can take for 
/■(e) IS ae^, where fi is some positive constant ; so that the form of ex- 
pression for the kinetic energy may be taken as 

Now let us go on to the case where we have two electrified bodies present, 
with charges e and e' of electricity ; let m and m' be their masses, q, q' 
their velocities, of which the components parallel to the axes of x, y, z 
nre (n, v, w)' ("'' ''^' ■> '^') respectively, the co-ordinates of the particles 
being (.r, ?/, z), (a;'_, 7/, s')- . 

If everything is symmetrical, the expression for the kinetic energy, 
if it only involves second powers of the charges of electricity, will be of 
the form 

\m(^ + \mcp + cie-^^ + /5e'^ ^'^-f-ee' k ./ {u, v, iv, «', v', w'} 

where/ (it, v, xv, n', v', iv') is a quadratic function 0? u, v, lu, u', v', w'. 

By Lagrange's equations we see that the last term will give rise to a 
force parallel to the axis of .r on the particle whose charge is e equal to 

I. dx dt du J 

with similar expressions for the forces parallel to ij and z. We can 
see, by substituting in this expression, that we get Weber's law if we 
make 

/ = - < (lo — u') + 2 ^ [v — v') + (to ~ w') \ ; 

r I r r r J 



ON ELKCTRICAL THEORIES. 113 



Riemann's law, if we make 



/= I {(u - ti'y + (v- v'y + (w - w'y] ; 

Clansins' law, if we make 

f-=~ {mm' + vv' + ww'\ ; 

and that we cannot get Gauss's law in this way ; this is in accordance 
with the fact that Gauss's law does not satisfy the principle of the 
conservation of energy. This way of considering the theories enables us 
to see that neither Weber's nor Riemann's formulae can be right, for if 
they were, an electrified body, when in presence of another, would, under 
certain circumstances, behave as if its mass were negative. Thus take 
Weber's law as an example : let us suppose that two electrified bodies are 
moving along the line joining them, which we may take as the axis of x ; 
then the expression for the kinetic energy, putting in the value of / which 
corresponds to Weber's law, is 

so that if im + ae2 + ^ 

r 

be negative, then the coefficient of if- in the kinetic energy will be nega- 
tive, and the body will behave as if its mass were negative ; and, by 
sufficiently increasing e' or diminishing r, we can make this expression 
negative, so that Weber's law leads to results which are inconsistent with 
experience. This result of Weber's law was first pointed out by Helmholtz. ' 

Exactly the same objection applies to Riemann's theory, and indeed 
we see that it will apply to any theory which makes the force between 
two electrified bodies depend on relative velocities and accelerations. 

The same objection need not apply to Claasius' theory, for substitut- 
ing the value of/ belonging to his theory, the kinetic energy equals 

{\m + ae2)22+ (i„i' + /3e'2)2'2 + ^^^, qq' cos e 

r 
so that the kinetic energy will be always positive if 

ilm + ae') (hn' + l3e'^)>ff£l^. 
This condition will evidently be satisfied if 

and this relation does not involve the electrification. We cannot assume 
that we can make r so small that this condition is not satisfied, for r has 
a minimum value depiending upon the shape and size of the electrified 
bodies. For example, if these are spheres, r cannot be less than the 
sum of their radii. On the other hand, a and /3 may be functions of the 

' Ueber die Tlworie der EleUrodynamik. Crelle, vol. Ixxv. p. 635 • Collected 
Works. Bd. I, S. 647. 

1885. 



114 BEPOET — 1885. 

sizes of tte electrified bodies, and the geometrical relations may be such. 
that the condition written above must be always satisfied. 

Fliysical reasons why the force between two electrified bodies should depend 
on their velocities and accelerations. 

If we assume Maxwell's hypothesis that a change in the electric 
polarisation produces the same effect as an electric current, then we see 
that the kinetic energy of an electrified body must be different from the 
kinetic energy of the same body moving at the same rate but not electri- 
fied. For let us suppose that we have an electrified body at rest, and 
consider the amount of work necessary to start it with a velocity q^. It 
is evident that it will be greater than when it is not electrified, for when 
it is electrified and in motion the electric polarisation in the surrounding 
dielectric will be in changing, and so in addition to starting the body 
with a velocity q we have, if Maxwell's hypothesis be true, to establish 
what is equivalent to a field full of electric currents. The production of 
these currents of course requires work, so that more work is required to 
start the body with a velocity q when it is electrified than when it is not ; 
in other words, the kinetic energy of a moving electrified body is greater 
than that of one not electrified, but under similar conditions as to mass and 
velocity. In fact in this case electricity behaves as if it possessed inertia. 

In a paper published in the ' Philosophical Magazine,' April 1881, I 
have shown that the kinetic energy of a charged sphere of radius a and 
mass m moving at a velocity q 

where /z is the magnetic permeability of the surrounding dielectric and 
e the charge on the sphere. If there are two spheres in the field, then 
I have shown in the same paper that the kinetic energy 

— 2^2 +TT ~r 2 + 2'" 1 + T5 — T 2 + 3~^ 22 COS f, 

a a sst 

where corresponding quantities for the two spheres are denoted by plain 
and accented letters. We see from this expression that the forces 
between the spheres are exactly the same as those given by Clausius' 
formulae. It would not, however, be legitimate to go and develope the 
laws of electrodynamics from this result in the way that Clausius does, 
as Clausius' conception of an electric current does not accord with that 
of the displacement theory. We may remark that in this case the part 
of the kinetic energy due to the electrification is always positive. 

On theories which are based on dynamical considerations, hut which 
neglect the action of the dielectric. 

F, E. Neumann ' was the first to develope a theory founded on the 
principles of the Conservation of Energy. His theory was based upon 
the assumption that two elements of circuit ds, Js', traversed by currents 
I, i' possess an amount of energy equal to 

a^ijLss^ dsds', 

r 

' ' Die mathematischen Gesetze der inducirten electrischen Strome,' Schriften der 
Berliner Academie der Wissemch., 1845. 



ON ELECrBICAL THEOBIES. 115 

where A is a constant which depends upon the unit of current, r is the 
distance between the elements, and e the angle between their directions. 
F. E. Neumann showed that this assumption leads to the same law of 
force between two closed circuits as that given by Ampere, and also ex- 
plained by means of it the induction of electric currents, v. Helmholtz ^ 
has investigated the most general expression for the energy possessed by 
two elements of current which is consistent with the condition that the 
force between two closed circuits should be the same as that given by 
Ampere's theory. We shall consider this theory in detail, as it includes 
all theories of this class, and we shall wish to refer to it when we come 
to discuss the relative merits of the various theories, v. Helmholtz 
hegins by showing that the most general expression for the energy of two 
elements of circuit consistent with Ampere's laws for closed circuits is 

1 A^L^ 1(1 ^ ^) (508 £ + {1-1) cos e cos &} ds ds', 

where 9 and 6' are respectively the angles ds and ds' make with the line 
joining the elements, ^ is a constant, and the other symbols have the same 
meaning as before. 

Let us call this quantity T ; then we know thatT denotes the existence 
•of a force dT/dr or 

- i ^—^ {(1 + ^) cos £ + (1 - h) cos d cos 8'} ds ds' 

along r, and a force — dT/rdd at right angles to r in the plane of ds and 
r, and in such a direction that it tends to diminish d ; this force equals 

i -^Ll^^l-k) fsin fl cos 6' + cos sin d' —^ ; 

rand since 

dd' ' 
^=cos ,, 

where rj is the angle between the plane containing r and ds and that 
containing r and ds', the transverse force 

A^ I i' 
= ^ 2 — 0-~^) W'^ " COS 0' + cos 9 sin 6' cos r)] . 

We see that these'forces will coincide with those assumed in Korte- 
weg's theory if the quantities a, I, c, d, which occur in that theory, have 
the following values : 

o= — A' 

b= -1(1 + ^^ A» 

d=^(l-k)A^. 

So that whatever ^be the value of /,-, these quantities", satisfy the con- 
•dition 

2a + b + c-2d= - .3A2. 

' Crelle, Ixxii, p. 57; Gesammeltc Werke, vol. i. p. 645. 

IS 



116 REPORT — 1885. 

According to Stefan, it is necessary if two circuits have a potential 

that 

2a+b-¥ c-2d=0. 

But Stefan did not consider the couple exerted by one element of 
circuit on another. The couples acting on the element els' will be as 
follows. There will be a couple tending to increase 6', i.e. a couple- 
whose axis is at right angles to both ds' and r, equal to dT/dd', i.e. to 



1 4li-L {(1 + Jc) sin cos & cos »,-2 cos 9 sin d'}, 

and another couple tending to increase v, i.e. a couple whose axis is along 
the line joining the elements equal to dT jdr), i.e. to 

1 A^ 



2 



(l + Z;) sin 6 sin 0' sin >;■ 



r 
"We see that these will agree with the couples in Korteweg's theory of 

r ' r r 

Let us return to the consideration of the energy of the circuits, and 
suppose that, instead of currents flowing along linear circuits, we have a 
distribution of them throughout space. If n, v, w be the currents in 
the element dx, dy, dz, then the part of the energy contributed by this 
element will be 

- A2 {[]u+Yv+Ww}'dx dy dz, 
where 

d^ dr) d^, 
with symmetrical expressions for V and W, where 

r^ = (x - ly + (1/ - vT- + (z - zy. 

We may write the expressions for TJ, V, W in the form 

v=i(i-A-)-^ + jj|^d^d,dc 

where4'= III {-% + - | + ^'^ |) ^'' ^"^ "^^ ■ 

If u, V, IV are the components of the ordinary conduction current, e the 
volume density of the free electricity, then 

du dv dw de \ 

dx dy dz dt' 

and if 1, m, n be the direction cosines of the normal to a surface at which 



ON ELECTKICAL THEOBIES. 117 

the currents become discontinuous, a the surface density of the electricity 
on this surface, then 

I (u—u^) + m (v—v^) + n (lu—xu^) -f __ = 0. 

(XiJ/ 

Remembering these equations, 4/ may be transformed into 

\\\ r —-dx dy dz + \\ r — - ds : 
JJJ dt -^ ^ ]] dt ' 

■or if (j> denote the electrostatic potential of the free electricity, we see 

\h ^ — ~ dx dy dz. 

^ 27r JJJ r dt ^ 

Substituting this value of ^ we find 

dxdt 
ay at 



We also see that 



^^W = (l-k)^-4.7riv. 
dzdt 



dx dy dz dt 



In order to get the equations connecting the electromotive force with the 
variation of the electrodynamic potential, Neumann made use of Lenz's 
law, and assumed that, since by that law the electromotive force tending 
to"'increase the current in an element of circuit moving with a velocity 
■w in the direction s would be of the same sign as 

— Xzy, 

where X is the force along s on the element per unit of length per unit 
of current flowing through it, it was actually equal to this quantity 
multiplied by a constant c, i.e. to 

— cKw; 

but if Ti ds be the energy of the element of current whose length is 
d&, and current strength i, 

X=^'^ 

and w=^ -=- ; 

dt 

so that the electromotive force per unit of length of the element 

__ ^ ds 
ds dt 

_ (IT 
-~'dT 



118 REPORT— 1885. 

V. Helmholtz has shown that it follows from the principle of the Conser- 
vation of Energy that if the energy in the elements dx, dy, dz, traversed 
by currents u, v, w, be 

A2 (TJu+Yv + Ww) dxdydz, 

then the components of the electromotive force parallel to the axes x, y, z 
respectively, due to the variation in the electrodynamic potential, will be 

-A^^, -A2'!Y, -A^^-^; 

dt ' dt ' dt 

the free electricity produces an electromotive force whose components are 

d<f) d<j> d<ji 
daj' dy' dz' 

so that the total electromotive force parallel to x, y, z 

dx dt 

Now if a be the specific resistance of the conductor, mi equals the elec- 
tromotive force parallel to the axis of .v, so that 

dx dt 

so that by the preceding equations 

47rl ^ \lxdtl dx dt* 

with similar equations for V, W. The quantities U, V, W and their 
first difierential coefBcients with respect to x, y, z are continuous, and 
these equations enable us to find them if we know the value of ^,. 
the potential of the free electricity. Helmholtz shows that the whole- 
energy in the field due to the currents may be written 

so that if h be negative, this expression may become negative, and in' 
that case the equilibrium would be unstable ; hence we conclude that 
only those theories are tenable for which /.■ is positive. 

The equations written above are those which hold in a conductor,, 
in an insulator the equations are 



r2 



■ ^=(i-"> Wit 



dz dt 

v. Helmholtz shows that in the conductor the electrostatic potential <^ 1 
satisfies the equation 



ON ELECTRICAL THEORIES. 119 

SO that if tlie conductor has an infinitely small resistance, the equation 



becomes 

v-»2 A — A 2?. 



V^(t> = A.Vc'^ 



This represents a wave motion, the velocity of propagation of which is 
l|A^yk. If 1c, as in ISTeumann's theory, be equal to unity, then the 
velocity of propagation is 1 /A, and from the value of A, found from 
experiments on the force between circuits conveying currents, this is 
nearly equal to the velocity of propagation of light. Thus, according to 
Neumann's theory, in a perfect conductor an electrostatic disturbance is 
propagated with the velocity of light. In an insulator satisfies the 
equation 

and this represents a motion propagated with an infinite velocity, and 
thus, according to this theory, an electrostatic disturbance is propagated 
with an infinite velocity in a perfect non-conductor. In an imperfectly 
conducting substance the velocity of propagation of a wave motion would 
depend upon the length of the wave. 

Let us now go on to consider, what, according to this theory, are the 
forces acting on an element of circuit conveying a current. Let us suppose 
that the element ds forms an element of a circuit through which a current 
t is flowing ; then the energy of the circuit will be 



J I as as ds J 



In order to find the force parallel to x, let us suppose that each element 
of the circuit receives an arbitrary displacement x, parallel to the axis of 
X ; then the alteration in the energy will be 

^,r f'i^'^+'^du^dWdzi^^^^^^.r^,^^^^ ■ 

J L dx ds ax US x as J } ds 

Integrating the second term by parts, we see that it may be written 

TA^ TJ^a;1 — A^ f t / ^U (?a; rfU */ c^ W cZs "1 , 
] \ dx ds dy ds dz ds J ' 

Substituting this value for the second term, we see that the alteration in 
the energy, 

= C-'-»3 + -f • { I (^J-f ) -S (f - f ) } - * ^ 

hence we see by the Conservation of Energy that there is a force on each 
element of current parallel to the axis of <c, equal to 

^ / dy /dV _dV\ _dz fdJJ _dW\ T . j 
l ds\dx dy J ds\dz dx J J ' 

and by symmetry forces parallel to y and z equal respectively to 
Jdz/'dW_dY\ dxfdY dV\ 1 ^2. 

Ldsvd;/ dz J ds\dx dyj j 
J^fd^_dW\_clyfdW_dV\l.^ 
\ ds\dz dx J ds\ dy dz) J 



120 EEPORT — 1885. 

so that the resultant of these forces is at right angles to the element. In 
addition to these forces there are other forces at places where the quantity 
lU is discontinuous, or, since U is continuous, at places where i is discon- 
tinuous, whose components parallel to the axes of x, y, z, are respectively 

A2[J?(, A2V^\, A^W^i; 

bnt II equals de/dt, the rate at which the free electricity is increasing 
at the place, so that we have at any place where the free electricity is 
changing a force whose components are 

dt 

A2V 

dt' 

A^W^^ 
dt 

We saw before that the force acting on the circuit per unit length is 
at right angles at each point to the element of circuit at that point, so 
that, unless a circuit includes places at which the quantity of free electri- 
city is changing, the circuit will behave as if it were acted on by forces 
which were everywhere normal to the elements on which they act. In 
the experiments which have been made to test whether the force on the 
element is at right angles to it, there have been no points where the free 
electricity is changing, so that these experiments do not contradict Neu- 
mann's theory, although, according to it, the force on an isolated element 
is not necessarily at right angles to that element, for in addition to the forces 
normal to the element we have forces equal to A^UcZe jdt, A?Yde j dt, A^W de/dt 
parallel to x, y, z respectively, acting at the ends, the resultant of these 
two forces is a force whose components parallel to the axes of x, y, z are 
respectively 

A^dedUds 
dt ds 

A^dedVds 
dt ds 

A^dedWds 
dt ds 

and as these forces are not necessarily at right angles to the element, the 
resultant force is not necessarily so ; the eifect of these forces could not, 
however, be detected unless there was a discontinuity in the current. 

V. Helmholtz in the memoir ' which we have already quoted shows 
that, according to his extension of F. E. Neumann's theory, the forces 
between two elements of circuit ds and ds' may be looked upon as made 
up of — 

(1) A i-epulsive force on ds due to an end of ds', equal (per unit 
length) to 

. , de'l dr 
atrds 

" Ueber die Theorie der EJelitrodynaviih, dritte Abhandlung, Crelle, Ixxviii. pp. 273, 
324, 1874; Gesammelte Werke,^. 723. 



ON ELECTRICAL THEORIES. 121 

(2) A repulsive force on ds due to ds', equal per unit length to 

^ < 2 cos (tZif ds') — 3 cos {r ds) cos (r ds') > ; 

(3) A repulsion between the ends of ds and ds', equal to 

- ^(1 + *) ^' If ^ 

(4) A repulsion on ds', due to an end of ds equal per unit length to 

— A^t'^-^. 
dt r ds 

The second of these is the only one considered in Ampere's theory. We 
must remember in calculating these forces that each element has two 
ends. 

Let us now go on to find the couples acting at each point of the 
circuit. If the tangent to the circuit makes an angle with the axis of z, 
and the plane containing the tangent and the axis of z an angle f with 
the plane of xz, then we may write 

-^ = sin cos 0, 
ds 

-^ = sin 6 sin d>, 
as ' 

dz a 

-— = cos 0, 
ds 

so that with the same notation as before the energy equals 

A^f. ru^+v$ + wtV> 

J V 'Is ds dsj 

= A^ £ (U sin e cos ^ + V sin sin (/) + W cos 0) ds, 

so that if ^ increase by c^, the alteration in the energy equals 
A^ I I ( — U sin 9 sin ^ + V sin cos ^) h<p ds, 

so that the couple tending to increase (j>, i.e. the couple whose axis is 
parallel to the axis of z, equals 

A^ I (V sin d cos <^ — U sin sin <^) 
per unit length of current ; this may be written 



A^ ("vt - U^V 
\ ds dsJ 



hence the couples parallel to the axes of y and x are by symmetry re- 
spectively 



I ds ds J ' 

A^i Iw'^-V^\. 
I ds ds J 



122 REPOET — 1885. 

Tlae axis of the resultant couple is perpendicular to the element and to 
the vector whose components are U, V, W. 

In another paper • v. Helmholtz discusses the force acting per unit of 
volume on a conductor traversed by electric currents ; he shows that, 
according to the potential theory, if u, v, w are the components of current 
through an element clx cly dz, and X, Y, Z the components of the force 
acting on this element of volume per unit of volume, then 

V A,r C^^ ^U\ AiW cZU\ ^del 

^=^'bU-dy) + ^[^.-d-J + ^dij 

^ . r fdXJ dV\ /dW dy\ „ del 

rr . , r /"'^U c?W\ (dY dW\ ^ del 

He then discusses the application of the potential law to sliding contacts, 
that is, contacts such as those made by a wire dipping into mercury ; in 
the derivation of the forces from the potential law it is assumed that the 
displacements are continuous, and it might be objected that we have no 
right to apply the law in this case as the motion of the wire and the 
mercury seems at first sight discontinuous, v. Helmholtz, however, 
points out that, as the wire carries the mercury with it as it moves, the 
motion is not really discontinuous and that Neumann's law is applicable. 
The question of sliding contacts comes prominently forward when we 
compare the various theories ; we shall return to it again in this con- 
nection. 

V. Helmholtz also in this paper investigates the electromotive foi'ces 
acting on a conductor in motion ; he shows that if the components of the 
velocity of the conductor at any point are a, /3, y, then P, Q, R, the com- 
ponents of the electromotive force, are given by the equatioit 

„ - /dU dV\ /dXJ dW\ d ^^^ ^^ ^ ^ 

with similar equations for Q and R. 

He also investigates the difference between the results of Ampere's 
and Neumann's theory for the E.M.F. due to induction. The results are 
complicated ; for practical purposes it is sufficient to notice that when 
there is a mechanical force tending to make the body move in a certain 
direction, there must be an E.M.F. when the body moves in that 
direction. 

C. Neumann^s Theory. 

C. Neumann assumes that the electric potential energy is propagated 
with a finite velocity, and that if two electrified bodies are in motion, the 
mutual potential energy is not ee'/r, where r is the distance between them, 
but ee'/r', where r' is the distance between them at a time t before, 
where t is the time taken by the potential to travel from the one body to 
the other. 

The energy considered in C Neumann's theory is a kind of energy 
quite different from any that we have experience of; it is not poten- 

' Ueher die Theorie der Elehtrodynamik, Crelle, Ixxviii. pp. 273-324, 1874 ; 
Gesammelte Werke, vol. ii. p. 703. 



ON ELECTRICAL THEORIES. 123 

tial energy, because that at any time depends only on the position of the 
system at that time ; it is not kinetic, because that depends only on the 
position and velocity of the system at the time under consideration, 
■whilst Neumann's energy depends on the velocity and position of the 
system at some previous time. In spite of ail this, however, Neumann 
applies the ordinary dynamical processes to this energy just as if it were 
kinetic or potential ; and in this way arrives at the same expression as- 
Weber for the force between two moving electrified bodies. The rest of 
the theory is the same as Weber's, except that Neumann's assumption 
about the nature of a current is different from Weber's. According to 
Weber, an electric current consists of equal quantities of positive and 
negative electricity, moving with equal velocities in opposite directions. 
According to Neumann, the positive electricity alone can move, the nega- 
tive being attached to the molecules of the conductor. Riecke and Clausius 
have shown that with this assumption and Weber's law a steady current 
must exert a force upon a particle at rest and charged with electricity, and 
must in consequence produce an irregular distribution of electricity over 
any conductor in its neighbourhood. 



Theories tohicli are founded on dynamical considerations and which take 
into account the action of the dielectric. 

In the theories we have hitherto considered, the influence of the 
medium which exists between the currents has been left altogether out of 
account. In the theories which we shall now proceed to discuss, the in- 
fluence of this medium is taken into consideration. This is, perhaps, the 
most important step that has ever been made in the theory of electricity, 
though from a practical point of view it is comparatively of little import- 
ance ; in fact, for practical purposes almost any one of the preceding 
theories will satisfy every requirement. 

Faraday was the first to look upon the dielectric as an important 
agent in electrical phenomena ; he was led to this by his desire to get rid, 
as far as possible, of the idea of action at a distance, which was so pre- 
valent in his time, but to which his researches have given the death-blow. 
In his ' Experimental Researches,' § 1164, speaking of electrostatic in- 
duction, he says, ' I was led to suspect that common induction itself 
was in all cases an action of contiguous particles, and that electrical 
action at a distance (i.e. ordinary inductive action) never occurred except 
through the influence of surrounding matter.' And later on he gives his- 
views as to the nature of the efiect in the medium; in § 1298 of the- 
' Researches ' he says, ' Induction appears to consist in a certain, 
polarised state of the particles into which they are thrown by the electri- 
fied body sustaining the action, the particles assuming positive and 
negfitive points or parts, which are symmetrically arranged with respect 
to each other and the inducting surfaces or particles. This state must 
be a forced one, for it is originated and sustained only by force, and 
sinks to the normal or quiescent state when that force is removed. It 
can be continued only in insulators by the same portion of electricity, 
beca.use they only can retain this state of the particles.' He gives an ex- 
perimental illustration of his view in § 1350. He says, ' As an illustration 
of the condition of the polarised particles in a dielectric under induction 
I may describe an experiment. Put in a glass vessel some clear rectified 



124 EEPOET— 1885. 

oil of turpentine, and introduce two wires passing tlirough glass tubes, 
when they coincide with the surface of the fluid and terminating in balls 
or points. Cut some very clean dry white silk into small particles, and 
put these also into the liquid ; then electrify one of the wii'es by an 
ordinary machine and discharge by the other. The silk will immediately 
gather from all parts of the liquid and form a band of particles reaching 
from wire to wire, and if touched by a glass rod will show considerable 
tenacity ; yet the moment the supply of electricity ceases the band will 
fall away and disappear by the dispersion of its parts. The conduction 
by the silk is in this case very small, and after the best examination I 
could give to the effects, the impression on my mind is that the adhesion 
of the whole is due to the polarity which each filament acquires, exactly 
as the particles of iron between the poles of a horse-shoe magnet are held 
together in one mass by a similar disposition of forces. The particles of 
Bilk therefore represent to me the condition of the molecules of the 
dielectric itself, which I assume to be polar, just as that of the silk is. 
In all cases of conductive discharge the contiguous polarised particles of 
the body are able to effect a neutrahsation of their forces with greater or 
less facility, as the silk does also in a very slight degree. Further we are 
not able to carry the parallel, except in imagination ; but if we could 
divide each particle of silk into two halves, and let each half travel until 
it met and united with the next half in an opposite state, it would then 
exert its carrying power (1307), and so far represent electrolytic 
discharge.' 

And it is not only in statical electricity that Faraday recognised the 
importance of the dielectric. When he is discussing his discovery of the 
induction of currents, which he ascribes to the assumption of what he 
called the electrotouic state by the body in which induced currents are 
developed, he says, § 73, ' It may even exist in non-conductors,' that is, 
that there is an electromotive force acting on the surrounding dielectric 
due to the variation in the primary current. Again, in § 1661, he says, 
* Now though we perceive the effects only in that portion of matter which, 
being in the neighbourhood, has conducting properties, yet hypotheti- 
cally it is probable that the non-conducting matter has also its relations 
to, and is affected by, the disturbing causes, though we have not yet dis- 
covered them. Again and again the relation of conductors and non- 
conductors has been shown to be one, not of opposition in kind, but only 
in degree (1334, 1603) ; and therefore for this, as well as for other 
reasons, it is probable that what will affect a conductor will affect an 
insulator also, producing, perhaps, what may deserve the term of the 
electrotonic state (60, 24"2, 1114).' And though he was unable to detect 
these effects experimentally, the following paragraph (1728) shows that 
his belief in their existence was not shaken : ' But then it may be asked. 
What is the relation of the projierties of insulating bodies, such as air, 
sulphur, or lac, when they intervene in the line of magnetic action ? 
The answer to this is at present merely conjectural. I have long thought 
there must be a particular condition of such bodies, coi'responding to the 
state which causes currents in metals and other conductors (26, 53, 191, 
201, 213) ; and considering that the bodies are insulators, one could 
expect that state to be one of tension. I have, by rotating non-conduct- 
ing bodies near magnetic poles, and poles near them, and also by causing 
powerful electric currents to be suddenly formed and to cease around 
and about insulators in various directions, endeavoured to make some 



1 
I 



ON ELECTRICAL THEOraES. 125' 

sncli state sensible, but have not succeeded. Nevertheless as any such 
state must be of exceedingly low intensity, because of the feeble intensity 
of the currents which are used to induce it, it may well be that the state 
may exist, and may be discoverable by some more expert experimentalist, 
though I have not been able to make it sensible.' 

Maxwell was the first to express Faraday's ideas in mathematical 
language. In his papers on ' Physical Lines of Force ' in the ' Philoso- 
phical Magazine ' for March, April, May, 1861, and January, February, 
1862, he developes a theory of electricity according to which the enero-y 
of the electro-magnetic field resides in the dielectric as well as in the con- 
ductors ; later, in the ' Philosophical Transactions ' for 1865, he greatly 
extended Faraday's ideas as well as put them into definite mathematical 
language, and this without reference to any special theory of the mechan- 
ism which produces electrical phenomena. We shall devote some time to 
discussing Maxwell's theory, as it is freer from serious objections than any 
other, while at the same time it covers a much wider ground. 

We shall begin by referring to Maxwell's view of the state of the 
dielectric in the electric field. Maxwell supposes that the dielectric i& 
changed, and perhaps the clearest way of describing this change is that 
of Faraday in the extract already quoted. Maxwell's nomenclature as to 
this change is a little unfortunate ; instead of speaking, like Faraday, of 
the polarisation of the dielectric, he speaks of the change as consistino- 
of an electric displacement, which in isotropic media is in the direction oi 
the electromotive force. Mathematically the two things are identical • 
we may either say of a wire that it is negatively electrified at one end a' 
and positively at the other end B, or else that there is a displacement of 
positive electricity from A to B, so that there is an excess of positive 
electricity at B and a deficiency at A. But though the words in a mathe- 
matical sense are identical, still the word displacement seems to connote 
special qualities which limit the generality of the conception in an unde- 
sirable way ; the word displacement seems to imply motion in the direction 
of displacement, while polarisation only implies that there is a vector 
change of some kind in the dielectric. The condition of the dielectric is 
quite analogous to the state of a piece of soft iron placed in a magnetic 
field. The polarisation or displacement is in isotropic media in the direc- 
tion of the_ electromotive force and proportional to it, just as the magnetic 
induction in isotropic media is in the direction of the mao'netic force and 
proportional to it. It was this proportionality combined with the fact that 
as soon as the electromotive force is removed the dielectric sprino-s back, 
as it were, to its original state, that led Maxwell to use the word dis- 
placement. He looked on the case as analogous to that of an elastic 
solid, which springs back to its original position when the external force 
is removed, and in which the displacement is proportional to the im- 
pressed force. To avoid any unnecessary definiteness we shall use the 
term dielectric polarisation instead of electric displacement. Thus 
according to this view the dielectric in the electric field is polarised. 
This polarisation means change of structure of some kind, and to produce 
this change of structure work is required. The energy in the polarised 
dielectric will be greater than the energy when it was unpolarised, for if 
the energy were less the dielectric would go into the polarised condition 
of itself, without the application of any external forces. 

It is rather difficult to see what is meant in Maxwell's theory by the- 
phrase ' quantity of electricity.' According to the old two-fluid theory 



126 BEPORT — 1885. 

an electrified body was supposed to contain a certain quantity of some- 

-thing called electricity, rules were pven for measuring this quantity, 

and the phrase ' quantity of electricity ' meant something quite definite. 

In Maxwell's theory, where everything is referred to the dielectric, the 

meaning of the phrase is not so obvious. We can, however, arrive at 

some idea of what is meant by the consideration of what are called ' tubes 

of force.' Let us suppose at first that the dielectric is air. A line of 

force is a line whose direction at any point coincides with the direction of 

the electromotive force at that point, so that we may conceive the electric 

•field to be filled with lines of force. If we consider the lines of force 

passing through some small closed curve, they will form a tube, and such 

a tube is called a tube of force ; and if the dimensions of the tube are such 

that the product of the cross section at any point and the electromotive 

force at that point is constant and equal to iir, the tube is called a unit 

-tube. We may thus conceive space to be filled with unit tubes of force. 

Since the electromotive force inside a conductor vanishes these tubes will 

end at the surface of a conductor. And the quantity of electricity on the 

conductor will be equal to the excess of the number of lines of force which 

leave the conductor over those which enter it. A tube is said to leave the 

conductor when the direction of the electromotive force is along the normal 

vdrawn outwards, and to enter it when the direction of the electromotive force 

is along the normal drawn inwards. As the conductor moves about it may 

be supposed to carry the tubes of force along with it, so that the number of 

tubes which end on the conductor remains constant. This way of look- 

ino- at electrification is quite satisfactory as long as we keep to one 

dielectric air ; when we have to consider difi'erent dielectrics it requires 

modification, because the electromotive force changes abruptly as we pass 

from one dielectric into another, so that a tube which was a unit tube in 

-one dielectric is not so in another. It is easy, however, to extend the 

definition of unit tubes so as to meet this difficulty ; for if the tubes pass 

from one dielectric A into another B the ratio of the product of the cross 

■section and electromotive force is constant for all the tubes and depends 

only on the nature of the dielectrics ; this ratio is the ratio of the specific 

inductive capacities in B and A. Air is taken as the standard dielectric, 

and the specific inductive capacity of another dielectric A is the ratio of 

the product of the electromotive force and cross section of a tube in air 

to the product of the same quantities for the same tube in the dielectric 

A. Thus if we amend our definition and say that a circuit tube is one 

such that the product of the cross section, the electromotive force, and the 

specific inductive capacity of the medium in which the cross section is 

situated is equal to 4?r, then the quantity of electricity on a conductor is 

equal to the excess of the number of unit tubes which leave the conductor 

over the number of those which enter it. In this way we get an idea of 

Vi^hat is meant by ' quantity of electricity ' in Maxwell's theory. Maxwell 

accounts for the forces observed between electrified bodies by a system 

of stresses in the dielectric separating them ; as, however, at present we 

wish to compare Maxwell's theory with other theories which do not 

touch upon this point, we shall discuss this part of the theory separately 

later on and go on to discuss those points which are involved in all the 

theories. 

The next great point in Maxwell's theory is the development of 
Faraday's remark that the electrotonic state may exist even in non-con- 
•ductors, i.e., that the dielectric surrounding a changing current is acted 



I 



I 



ON ELECTRICAL THEOEIES. 127 

•on by electromotive forces which polarise it. This statement is one as 
to whose truth nobody seems to entertain any doubt, whilst the state- 
ment that changes in the dielectric polarisation produce effects analogous 
to those produced by ordinary conduction currents is by no means so 
universally received, and yet the one seems the necessary consequence of 
the other. If we regard the whole electric field as a dynamical system, 
and to fix our ideas consider an element a of the dielectric, and the cur- 
rent, which is supposed to vary, then, since a variation in the current 
polarises a, i.e., produces a change in its structure, there must be 
mechanism connecting the current with the element a ; but if this is so 
then it follows from dynamical principles that a non-uniform variation 
in the structure of rt must produce a change in the current — in other 
words, that a change in the rate of change of the polarisation of a pro- 
duces an electromotive force on the current, i.e. that the change of polarisa- 
tion produces an effect analogous to that of an ordinary conduction 
current. We may illustrate this by a purely dynamical example. Sup- 
pose we have a dynamical system defined by two co-ordinates p and q, 
and let T be the kinetic energy of the system and V the potential energy ; 
then by Lagrange's equation the force tending to increase q 

= - ^+ cZT__cZ^ dT 
dq dq dt dq' 

Now if there is a force tending to alter q which depends upon the 
acceleration of p, there must be a term in the kinetic energy of the 
form 

but if we apply Lagrange's equations to the p co-ordinates we see that 
•this term implies the existence of a force tending to increase p equal to 

-lit ^^' 

so that an acceleration of q will produce a force tending to alter p. 
To make this applicable to the case of the current and the dielectric, we 
have only to suppose that p represents the current, q the polarisation of 
the dielectric. That a change in p produces a change in q is shown by 
the fact that the dielectric is polarised when the current is changing, and 
this shows that there must be a term of the form A.pq, in expression for 
the kinetic energy ; from this it follows that a change in q, i.e., in the rate 
of change of the polarisation, will produce an E.M.F. on the circuit. As 
the variation of the dielectric polarisation produces the same effect as a 
conduction current, we must in the case, when both conduction current 
and alteration in the polarisation are present, look upon the true or effec- 
tive current as the sum of the conduction current and the change in the 
polarisation. 

The components/, g, h of the dielectric polarisation are defined by the 



equation 



/=^x 9=~Tr h=^Z, 

4n- 47r 4n- 



where K is the specific inductive capacity of the medium, X, Y, Z the 
components of the electromotive force. If u, v, w are the components 
of the effective current, p, q, r the components of the conduction 



128 KEPOET — 1885. 

current, then Maxwell in his paper on a ' Dynamical Theory of the 
Electromagnetic Field,' ' Phil . Trans., 1885,' puts 

Since ^ + 1^ + ':^r = _ ^ 

dx dy dz dt 

, df . da dh 

and -jL + ^ + -r-= P^ 

ax ay dz 

■where p is the volume density of the free electricity, we see that 

du dv div p. 

dx dy dz 

If the values of the quantities in a medium A be denoting by putting 
the suffix 1 to the symbols representing them, and those in another 
dielectric B by putting the suffix 2, then if I, m, n are the direction 
cosines of the normal from A to B, we have at the boundary of the two 
media 

^ (ih-p-i) + m (qi-q^) + n (ri-ra) = ^ 

^ (/i -/2) + ''* (ui -Oi) + '^ {K-1h) = -<^, 

where (r is the surface density of the electi'icity ; thus 

I (ui—u^) + 111 (V1—V2) + n (W1 — W2) =0; 

so that u, V, iv satisfy the same equations as the components of the velocity 
of an incompressible fluid. 

This assumption about the magnitude of the effects produced by the 
alteration in the dielectric polarisation makes the mathematics of the 
theory as simple as possible. If Maxwell had merely assumed that the 
alteration of the dielectric polarisation produces effects analogous to those 
produced by ordinary conduction currents, and that the equivalent con- 
duction current was proportional to the rate of alteration of the dielectric 
polarisation, then these equations would have been 

, dY 

"=^+"^' 
^ dZ 

so that in a homogeneous dielectric 

du dv dw '''^ / 1 _ 4 """ "l 

d^ ckf ih dt\ TJ' 



Z(w,— 1*2) + m. {v^—v^) + n {w^—Wi) = y+a^ 



dT , dN, dlif 



It ' dt ^ dt 

where N is the component of the electromotive force normal to the 
surface . 



ON ELECTRICAL THEOEIES. 129 

Maxwell's assumption is that a=K/47r, and this makes the equations 
much simpler ; it is, however, important to remember that Maxwell's 
theory of the dielectric involves the two assumptions— 

1st. That alterations in the dielectric polarisation produce effects 
analogous to those of ordinary conduction currents ; 

2nd. That the magnitude of the equivalent conducting current 

= d I -— F V Idt, where F is the electromotive force at the point ; this is 

equivalent to saying that all the currents are closed currents, and that 
there is no discontinuity in them. 

Maxwell developes his theory by means of the principle of the Con- 
servation of Energy. 

Let us consider an electric field full of currents, whether ordinary 
conduction currents or polarisation ones. Then this field may be looked 
upon as a material system, and all the phenomena have to be explained as 
the effects of the motion of this system ; a current must be looked upon 
as a change in the structure of the system, and so capable of representa- 
tion by means of the differential coefficients of the co-ordinates fixing 
the system ; we can thus represent the current at each point as the 
differential coefficient of some generalised co-onlinate fixing the system ; 
the components u, v, w of the current passing through an element dx, 
dy, dz may be looked upon as the rates of change of some generalised 
co-ordinates ; we may write the energy as 



if 1 1 (Fm + Gv + B.w}dx dy dz, 



where F, G, H may be looked upon as momenta corresponding to 
u, V, w. It remains to identify F, G, H with known quantities. Maxwell 
does this by the aid of Faraday's result, that the electromotive force 
round a circuit equals the rate of diminution of the number of lines of 
force passing through it. 

Let us consider a single linear circuit in which the current is i, or 
say dqjdt, then the energy 

= ^J^h^- + G^+-B^\ds, 
J at L ds ds ds J 

where ds is an element of circuit ; but by Lagrange's equation the force 
tending to increase q, i.e., the electromotive force in the circuit, 

= -^{(F'^^+GiM+K^')ds; 
dtj\ as ds ds) 

so that ffF ^4- G'i^+H^V* 

]\ ds ds ds) 

equals the number of lines of force passing through the circuit ; but if d^ 
be an element of surface closing up the circuit, I, m, n the direction cosines 
of the normal, then by Stokes' theorem 



f( 



F — + G^ + R—^ds 
ds ds dsj 



1885. 



ll{'{^-f)+-(f-f)-'(rf)}-^ 

E. 



130 EEPOET — 1885. 

but the number of lines of force passing through the circtiit 

= I (JO' + ini + nc)dS, 
■where a, h, c are the components of magnetic induction, so that 

dy dz ' 

dz dx 
^^dG_clF 

dx dy 

To connect a, h, c with the current, Maxwell makes use of the prin- 
ciple that the line integral of the magnetic force taken round any closed 
curve equals the current flowing through the curve. This leads to the 
equations — 

. dy dl3 

4;r«=— — — , 
ay dz 

. da dy 

dz ax 

A dft da 

dx dy 

so that if /u be the coefficient of magnetic permeability, 

. dc db 

dy dz 

and so on. Substituting the values of a, b, c, given above, we find 

dx I dx dy dz i 

with similar equations for G and H. 

Now V. Helmholtz, in his paper ' Ueber die Bewegnngsgleichungen der 
Elektricitat fiir ruhende leitende Korper ' (Crelle, Ixxii. p. 57 ; Gesam- 
melte Werke, ii. p. 545), has investigated the most general expressions 
for F, Gr, H, consistent with the force between two closed circuits agree- 
ing with that indicated by Ampere's theory, and he finds that if the 
circuits are closed circuits, as Maxwell assumes all circuits to be, then 

dx dy dz 
and therefore 477^^= — v ^F, 

with similar equations for G and H. These equations are sufficient to 
determine the quantities F, G, H. 

Maxwell does not at once put dFldx + dG/dy + dH.ldz=0; he writes 
for this quantity, and puts 

X= \—dx dy dz. 
Then F=JJ|^da; dy dz+-^; 



ON ELECTRICAL THEORIES. 131 

as, however, he subsequently puts J=0, we may at once simplify the 
equation by making this assumption. 
Since the kinetic energy equals 



1 ( [ [ (Fu + Gv + mu) dx dij dz, 



we see by Lagrange's equations that the electromotive force tending to 
increase u 

dt ' 

in addition to this there is the force arising from the electrostatic poten- 
tial (j), so that the total electromotive force parallel to the axis of x 

^_dF_d<j> 
dt dx 

so that if (s be the specific resistance of the substance, K its specific induc- 
tive capacity, then 

47r . dF d(^ 
''P=K^=-dt-Tx' 

'^ '"' ^'^dt Adt dxi 4:7r\dt^ dicdti ' 

tut we saw before that 

47r/i!{= — V ^F ; 

substituting for u this value, we see 

^^F^^fdY d^l Jd^ d^^ 
<r I dt ^dx / ^"^^ 1 dt^ ^dx dtr 

^ihus in the dielectric the equation becomes 

^idt^^dxdtr 



in the conductor 



o- \ dt dx i 



The equation for the dielectric shows that it represents a wave-motion 
propagated with the velocity 1/v/K^; the numerical value of this velocity 
agrees very approximately witla the velocity of light, and this led Max- 
well to the theory that the changes in the structure of the dielectric 
which take place when the dielectric is polarised are of the same nature 
as those which constitute light. This theory, which is called the electro- 
magnetic theory of light, might almost as justly be called the mechanical 
theory of dielectric polarisation. Earchhoff, in his paper ' Ueber die 
Bewegung der Blectricitat in Drahten ' (Pogg. Ann., vol. c. 1857 j 
-Gesammelte Werke, p. 131), was the first to point out that some elec- 
trical actions are propagated with the velocity of light. In this paper he 
considers the motion of electricity in wires whose diameters are small 
compared with their length. There are three things which have to be con- 
sidered in this problem — (1) the self-induction of the electric current, and 

k2 



132 REPORT— 1885. 

if the medium be taken into account, that of the polarisation currents in 
the dielectric. This self-induction produces very much the same effect 
as if the electric current possessed momentum— (2) the electrostatic action 
of the free electricity which tends to bring things to a definite state, and 
corresponds very much to the spring in a material system. Then, lastly, 
there is the electrical resistance, which corresponds to fi'iction in an ordinary 
system. We see from the analogy that if the resistance be small enough, 
the electrical system will vibrate ; if, however, the resistance is large, 
the electrical disturbance will be propagated in the same way as heat. 
Kirchhoff in his paper considers the propagation of electrical disturbance 
along a wire under various conditions : we shall only consider here one 
of these cases ; that of an endless wire. In his solution Kirchhoff only 
considers the self-induction of the current flowing along the wire ; he 
does not consider the effects in the surrounding dielectric. He shows 
that if e be the quantity of electricity per unit length of the wire, and 

e=X sin ns, 

where s is the length of a portion of the wire measured from some fixed 
point, then X satisfies the differential equation 

cPX c^r dX c2 d''X 



dt^ I6yl dt 2 ds^ ' 

where c is a quantity which occurs in Weber's theory, and is the velocity 
with which two charged particles must move if the electrodynamic 
attraction between them balances the electrostatic repulsion ; 

r is the resistance of the wire in electrostatic measure ; y = log If a, 

where I is the length of the wire and a the radius of its cross section. 
The form of the solution of this equation depends on the magnitude of 

If this quantity be large, the solution takes the form representing the- 
propagation of a wave along the wire with the velocity c/\/2. Weber's 
researches show that this velocity is very nearly equal to the velocity of 
light. If, however, the above-mentioned quantity be small, then the 
solution of the equation takes the same form as the formula which 
expresses the conduction of heat along the wire. We must not, however, 
take this to mean that the electric disturbance is propagated with an 
infinite velocity, so that if we had an infinitely delicate electrometer at a 
finite distance from the source of disturbance we could detect an electrifi- 
cation after an indefinitely short time, for it seems obvious that the 
electrical resistance cannot increase the velocity of propagation any more 
than the resistance of the air could increase the velocity of propagation of 
a disturbance along a line of particles connected by an elastic string. 
The conditions at the end help to determine the form of the solution, and 
these cannot make themselves felt until the disturbance has reached it ;. 
thus the heat form of solution probably only holds after a time from the 
commencement of the disturbance greater than the time taken by light 
to travel along the wire. If we take the case of a copper wire one square 
centimetre in area, we shall find that the wave form of solution will hold 
if the wire is not more than 100 miles in length, while the heat form 
will correspond to wires which are much longer than this. Kirchhoff's 



ON ELECTRICAL THEORIES. 133 

solution only refers to the propagation of a disturbance in a conductor, 
while Maxwell's refers to the propagation of such a disturbance in the 
dielectric. 

Maxwell considers the effect of the motion of the medium on the elec- 
tromotive force ; he shows that the electromotive force parallel to the 
axis of X 

where u, v, to are the components of the velocity of the medium conveying 
electric action. Here \p is not the electrostatic potential merely; it is 
equal, as Helmholtz has shown,' to the electrostatic potential plus the 
term 

Fu + Go + Hw. 

We must remark here that ti, v, lo are the components of the velocity of 
the medium conveying the electric action, i.e. the ether, and this need 
not necessarily be the same as the velocity of the dielectric. 

V. Helmholtz' s Dielectric Theory. 

V. Helmholtz, in the paper ^ to which we have so often referred, con- 
siders the effect of the polarisation of the dielectric ; he supposes that 
when an electromotive force X, parallel to the axis of «, acts on an 
element of a dielectric, it puts it into such a state that it produces the 
same effect as if there were electricity of surface-density x oii the face 
dy dz of the element, and an equal quantity of electricity of the opposite 
sign on the parallel face, x being given by the equation 

the variations in the electromotive forces acting on the dielectric are 
supposed to produce the same effect as ordinary conduction currents 
whose components are x, g, ^, where x, g, 5 are the components of a 
vector quantity which in isotropic media is parallel to the electromotive 
force and equal to the product of e and the intensity of the force. This 
agrees with Maxwell's assumption, provided 

£ = K/47r, 

where K is the specific inductive capacity of the dielectric. If <^ be the 
electrostatic potential of the free electricity, ;// the potential due to the 
polarisation of the dielectric, then Helmholtz shows that 



+ 



A |(l + 4;re)A(0-l-,/.) J=-4tE, 



where E is the volume-density of the free electricity. The corresponding 
equation in Maxwell's theory is of the same form, provided 

l-f- 47r£ = K. 

' Ueher die Theorie der Elehtrodynainih ; die eleJtirodynamisic'he Krdfte in 
hewegteJi Leitern, Crelle, Ixxviii. p. 309 ; Gesammelte WerJte, ii. p. 745. 

' Ueber die Theorie der EleMrodynamik, Crelle, Ixxii. p. 57; Gesammelte 
WerTie, i. p. 644. 



134 EEPOET — 1885. 

This relation seems inconsistent with the previous one ; it may, how- 
ever, be reconciled with it in the following way : — 

The potential dae to a quantity B of electricity at a point distant 
r from it is proportional to 

E 

If £o be the value of e for air, the potential under the same circumstances 
in air is proportional to 

E 
(l + 47reo)r' 

if, then, we define unit potential as the potential at unit distance from 
unit of electricity in air, the potential due to a quantity E in another 
medium will be 



r l + 47r£p -1 E 
1 l + 47r£ J r' 



We see that this is equivalent to increasing the unit of potential, and 
therefore the unit electromotive force, l+47r£o times, so that if we use 
the new unit the equations will be 



^~l+47reo ' 



d r l+47r£ cl ,^1 



= -47rE. 



These will coincide with Maxwell's equation if we make £ and cq each 
infinite and put K=£/fo. 

Returning to Helmholtz's theory, if u, v, w are the components of the 
total current 

u=p + x, 

where p, q, r are the components of the conduction current. 
Helmholtz puts 

du dv div dp 
dx'^dy '^dz~~dt' 

where p is the volume-density of the free electricity, and if <t be the 
surface-density of the free electricity at any point of a surface separating 
two media, ^^l, Vi, w-^; u^, v^, Wa the components of the current in the 
two media, I, m, n the direction cosines of the nonnal to the surface 
drawn from the first medium to the second, then according to v. Helm- 
holtz 

According to Maxwell the corresponding equations are 



du dv dw 

dx dy dz ' 

I (ui—U2)+m (vi—Vo)+n (iOi—W2)=0. 



ON ELECTBICAL THEORIES. 135 

As it is in the difference between these equations that the difference 
in the theory really lies, it will be instructive to look at them from 
another point of view. We know of no way in which the quantity of free 
electricity can be altered except by electricity being conveyed by con- 
duction cux-rents to the place where the alteration takes place. Assuming, 
then, that the alteration in the density is caused by such currents 

dp dq dr dp 
l^'^~d~y'^Jz~~di' 

I (Pi-P2)+m (2i-22)+« (ri-r2)=^. 

So that Helmholtz's equations taken in conjunction with these are 
equivalent to the condition 

dx dy dz ' 

Thus on Helmholtz's theory the dielectric currents behave like the 
flow of an incompressible fluid, while on Maxwell's theory it is the total 
current, which is the sum of the conduction currents and the dielectric 
currents which behave in this way. 

The equations we have arrived at for the dielectric currents seem 
inconsistent with Helmholtz's definition of them ; for since 

X=eX, 

with similar equations for p and 3, and since in a medium at rest 

dt dx' 

dt~dy' 
_dW_d(l, 
dt ~dz' 

where U, V, W are the components of the vector potential. If we consider 
a surface separating two portions of the same dielectric and coated 
with electricity whose surface-density is o-, we have, since U, V, W are 
not discontinuous on crossing the surface, 

d r d<t> dm ddr\2 

td<t) d(t> cZrf>"|2 
I ^ + m j-+n y denotes the difference between the values 

d(b d^ d<j> 
of I -J- + WT" + n -T~ on the two sides of the surface. 
ci3J ciy dz 

rU d<b d<t,f 1 

e da 
so that I {±^-x^)^m {■Qi-'Q^')^'^ (3i-32)=l+4;re dt^ 

and so cannot vanish if the surface-density of the electricity changes]; 



136 REPORT — 1885. 

thus Helmholtz's equation seems to be inconsistent with the principle 
that the change in the quantity of free electricity is caused by conduction 
currents. In the case above considered, Maxwell's equations lead to no 
difficulty ; it does not follow, however, that Maxwell's assumption that 
the total current behaves like the flow of an incompressible fluid is 
absolutely necessary. We shall consider later on the differences which the 
abandonment of this assumption will make in the theory. 

We shall now go on to consider Helmholtz's equations and compare 
them with the corresponding ones in Maxwell's theory. 

The quantities U, V, W are given by equation of the form 



U=J 



^^'-<t^\[ 



—d'E, dt) d^, 
r 



where h is the constant which we mentioned before as occurring in 
Helmholtz's theory, and 

where <f> is the electrostatic potential ; it follows from these equations 

that 

dJJ.dVdW , dd> 

- — T — — r — ^j — Ic ~i-. 

ax ay dz dt 

The corresponding equation in Maxwell's theory is 

dx dy dz ' 

60 that these equations coincide if ^=0. We can see from the value of x 
given on page 116 that, on Helmholtz's theory, this quantity would also 
vanish, whatever be the value of k, if the total current behaved like the 
flow of an incompressible fluid. 

If a, /3, y are the components of the magnetic force, then on Helm- 
holtz's theory 



ay dz Idtdx • J 



dy 

dz dx I dtdy J 

dx dy idtdz J 

where A is a quantity depending on the unit of current adopted, and is 
such that the force between two parallel elements of currents at right 
angles to the line joining them is 

l-^ijdsds', 

where r is the distance between the elements, ij the current through them, 
and ds ds' their lengths ; the corresponding equations on Maxwell's theory 
are 

dy_dl3 _, 

dy dz 

with similar equations for v and w. 



ON ELECTRICAL THEORIES. 137 

If X, n, V are the intensities of magnetisation, ■& tlie coefficient of 
induced magnetisation, the equations satisfied by the components of the 
dielectric and magnetic polarisation are of the type 

__4^r^(l±M)__A2^+ r ^ _ (l + 4:r^)(l + 4:r0 "1 d_ 
(i+47r£o) (l + 47rSo) dfi \ k I dx 

1 dx dy dz J 

^ ~ (l + 47r£o) (1+477^0) ■^' 

-where eq ^^^ ^0 ^re the values of e and S for air. 

These equations show that the dielectric and magnetic polarisations 
are propagated by waves. For the dielectric polarisation longitudinal 
waves are propagated with the velocity 

1 ; (l+47rO (I+^tteq) (l + 47r5o) \l. 
A I 47r£/j J 

Transverse waves are propagated with the velocity 



-V2 



+ 4;r£o) (l+47r^o) 



47re (l+47r3) 

Longitudinal waves of magnetic disturbances are propagated with 
an infinite velocity, and traverse ones with the same velocity as the 
transverse waves of dielectric polarisation. The electrostatic potential is 
propagated with the velocity IjAs/k. In Maxwell's theory the corre- 
sponding equations are 

where fx is the magnetic permeability and K the specific inductive capacity, 
so that for both dielectric and magnetic polarisation the velocity of the 
longitudinal wave is infinite, while the velocity of the transverse wave is 
l/s/fiK. The velocity of propagation of the electrostatic potential is 
infinite. If in Helmholtz's theory we put Z;:=0, •&o = 0, £/£o=K, while 
both £ and £0 are infinite, we see that the results of his theory will in this 
respect agree with Maxwell's. 

Though in Maxwell's theory the velocity of propagation of the electro- 
static potential is infinite, and in Helmholtz's theory 1/A\/A;, the electro- 
motive force at a point, and consequently the dielectric polarisation, does 
not travel with an infinite velocity in Maxwell's theory, or with the 
velocity 1/A\/ A; in Helmholtz's. We can see the reason of this nacre 
easily from Maxwell's theory, as the equations are simpler. 

Using the notation of that theory, viz.,/, g, h, for the components of 
the electric displacement, F, G, H for the components of the vector 
potential, and ^ for the electrostatic potential, then in a dielectric the 
equations are 

4<-rr . _ _ d¥ _ d(p 

K^ ~ ~dt "dx 



138 EEPORT— 1885. 

477 df_ _ tPF _ d^ 
'K dt~ 'dF' dxdt' 

but, since 47r/i ^= — v ^F, 

we see that ±^v^F='^ + ^. 

fi\L d.f' dxdt 

Now, since v ^^ = 0, a particular solution of tWs differential equation 
will be 

dt dx 

while the general solution will be the sum of this solution and the 
general solution of 

/iK dt^ 

The particular solution is propagated at the same rate as f, while the other 
part of the solution represents a wave travelling with the velocity 1 / V^K. 
Since the part of the solution which travels at an infinite rate satisfies 
the equation 

dt dx 
or f= 0, 

we see that the electromotive force due to the change in the vector 
potential just balances the electrostatic electromotive force, so that until 
the part of the vector potential which travels at the rate Ij s/fjiK comes 
up the resultant electromotive force vanishes. This explains how the 
electromotive force on Maxwell's theory travels at a different rate from 
the potential, and a similar explanation will apply to Helmholtz's theory. 
Helmholtz's equations for a conductor are 

a^hc= (1 +47r^) 47rA2 f^-^^ { V> + (1 + 4,r^-/.-) A^ || } 

where a is the specific resistance of the conductor ; on Maxwell's theory 
the equations are 

9 J du 

These equations differ by terms involving the unknown constant h; but 
V. Helmholtz's ' investigations on the motion of electricity along thin 
conducting wires show that there is not much hope of distinguishing be- 
tween the theories by experiments on conductors. We have seen that 
we can make certain equations which occur in Helmholtz's theory 
coincide with the corresponding ones in Maxwell's by giving par- 
ticular values to certain constants. The difference in Helmholtz's and 
Maxwell's views as to the continuity of the currents is too serious to let 
us expect that we should ever get a complete agreement between the 

' Zfeher die Ben-egvngsgleichxmgen der Elehtricitdt fiir ruheiide leitende Korper. 
Gesammelte Werke, vol. i. p. 603. 



ON ELECTRICAL THEOKIES. 139 

theories ; and, in fact, make as many assumptions about the constants as 
we may, there are still differences between the theories. 

In order to get as general a theory of these dielectric currents as 
possible, we shall investigate the consequences of assuming merely that 
these currents are proportional to the rate of change of the electromotive 
force, and write dielectric current^ r; (rate of change of the electromotive 
force), where ?/ is a constant which for the present is left indeterminate; 
In Maxwell's theory 7;=K/4n-, where K is the specific inductive capacity 
of the dielectric ; in Helmholtz's theory, i] is also proportional to the spe- 
cific inductive capacity. We shall denote the components of the dielec- 
tric currents by the symbols f, g, h; the components of the conduction 
current by p, q, r, and the components of the total current by ii, v, w, so 
that 

u=p +/. 
Let us put 

du , dv dw p 

dx dy dz ' 

I (ui—U2) + m (vi—V2) + n (wi—W2)=:^ ; 

on Maxwell's theory I" and 2 are each zero. 

If F, G, H are the components of the vector potential, then by 
V. Helmholtz's investigation of the most general expression possible for 
these quantities consistent with the condition that the forces between 
closed circuits should agree with those given by Ampere's laws, 

• ¥ = i(l-k)^+f.{{{'td^dnd^, 
with similar expressions for G and H, where Jc is a constant and 

Transforming this expression we see, using the same notation as before, 
that 

1/'= rfi{l («! — 1^2)+™ (yj— Vo)-!-^ (^1— ^^2)} ^^ 

= fLrS(iS- {{ fir P d^ dr, di;, 

where dS is an element of a surface at which there is discontinuity in 
u, V, w. 

Let us now consider the equations which hold in a perfectly insulating 
dielectric. 

The rate of change of the x component of the electromotive force in a 
medium at rest 

= _^ _ d^(p 
dt^ dt dx* 

where ^ is the electrostatic potential ; it also equals // rj, so that 

f__d^F_ d^(t> 
H dt'^ dt dx 



140 BEPOET — 1885. 

Since in this case there is no conduction current u =/, and the pre- 
ceding equation for F shows that 

substituting for/ 

if - — 1- , + -— - = Y, we get, by dififerentiating this expression, 

ax ay az ^ <=> •' 

with regard to x and the corresponding equations for G and H with 
regard to y and z respectively, and adding 

v=^x - i (1-^) vV = 4x,;x|A^X + I V^^ } . 

Now, as the dielectric is a perfect insulator, there are no conduction 
currents, so that the density of the free electricity remains constant, 
and therefore 

From the expression for yp we see that 

Substituting this value of v^J' in the equation for x, we get 

which represents the propagation of a normal wave with the velocity 

1/ V^Trrjk. 

The transverse wave is propagated with the velocity l/v4rr)7/j, so 
that if the view that light consists of electric or magnetic disturbances be 
correct, since experiment shows that this velocity is very nearly equal to 
l/'^Kfj., we must have 47rj; = K or ?j = K/47r, which is Maxwell's theory. 
So that if we assume that light is_an electric phenomenon, then in those 
mediain which its velocity = 1/n//uK Maxwell's theory that the electric 
cui'rents flow like an incompressible fluid must be true. 

If a, /3, y are the components of the magnetic force, then, since 



4 



F = 1 (1 - z;) ii + Mi'i m dr, di;, 



we see from Ampere's formula for the magnetic force due to a circuit 
that 

^^dH_dG _ dY 
dy dz dz ' 



ON KLECTRICAL THEOKIES. 141 

where V is the magnetic potential due to the magnetism in the field both 
permanent and induced. From these equations we get 

I dy dx j dz\. d.v dy dz J 

= _ 4;r,,i«+ ^ |i (1 _ /,) V^v^ - x} 

instead of the equation 

da dS . 

-— — = — 4!Trw. 

ay dx 

We have been obliged to introduce another assumption|liere, viz., that 
the magnetic force due to an element of current is given by Ampere's 
expression. 

We could not assume Maxwell's way of connecting currents with 
magnetic force, viz. that the total current flowing through any closed 
curve is equal to the line integral of the magnetic force round the curve, 
for the result can only be true when the currents flow like an incom-' 
pressible fluid. 

Let us now go on to consider the force acting on the medium convey- 
ing the current. 

If we consider a continuous distribution of currents, the kinetic 
energy 



— 2 



i i (F2i + Qv + B.w) dx dy dz. 



If we derive the force parallel to x by the variation of the energy in 
the usual way we find, just as in Helmholtz's paper, • that the force 
parallel to x 

I \dx dy) \dx dz) \dx dy^dljr 



or with our notation 



= V < 



\ dx dy J \ dx dz J ' 



and that on any surface where there is a discontinuity in the values of 
u, V, w there is a force equal per unit of area to 

F [I («i — u^) + m (i^i — v^) + n (w, — w^)} 
or F2. 

In the same paper it is shown that it follows from the principle of the 
Conservation of Energy that the force exerted by a distribution of cur- 
rents equals the force given by Ampere's expression along with a force 
at the point ^r)l^ whose component parallel to the axis of x equals 

\\\ (S + I ^ 1^) ^ (^' {^-^) + ^' (y - v)+w' (z-Oyxdydz 
■* J J V ^^' ~ "^'^ ■*■ '" ^^' ~ "^2) + '^ (^1 - ^i) ] ^-^^ G<'' (aJ - 

> Die eleUrodi/namischen Kr'dfte in hewegten Lcitern, Crelle, Ixxviii. p. 298 
1874, or Gesammelte Werke, vol. i. p. 733. 



142 itEPOET— 1885. 

or with our notation 

' "^^ [^1'' {x-D + v' (y - n) + w'(z- O) ^^ dy d^ 

+ W-"" ^T '(^^' («= - + ^' (y -v) + w' (z- o) ds, 

where u', v', w' are the components of the current at the point ^ rj ^; 
so that in addition to Ampere's forces we have additional forces 
wherever P and S have finite values. From the above expressions we see 
that any element where P has a finite value exerts a repulsive force equal 
per unit of volume to 

— ^ cos 6, 
r 

tending from the element ; where r is the distance of the element from 
the point at which the force is reckoned, i the intensity of the current at 
this point, and 6 the angle between the direction of the current and r. 
Any element of surface where S has a finite value exerts a repulsive 
force equal per unit of surface to 

V 

~' i cos y, 
r 

where the notation is the same as before. Of course none of these forces 
exist in Maxwell's theory. They could be most easily detected in cases 
where the part of the forces given by Ampere's theory vanishes as it 
would for the case of an endless solenoid. In this case, though the 
Amperian forces vanish, the forces due to the discontinuity in the current 
do not, so that if the endless solenoid were to move under the action of 
external currents it would denote the existence of discontinuity in the 
current. An experiment of this kind has been made by Schiller ; we 
shall discuss the results of it later. 

To sum up, the differences between the most general theory which 
takes into account the action of the dielectric, and Maxwell's, are — 

1. The existence of a normal wave in the general theory, but not in 
Maxwell's. 

2. The difference in the velocity of propagation of the transverse 
wave. 

3. The difference in the relation between electric currents and mag- 
netic force. 

4. The forces which arise from discontinuity in the currents. 

The Experimental Evidence as to tlie Truth of the various Theories. 

The theories we have considered may be divided into two great classes, 
according as they do or do not take into account the action of the dielec- 
tric surrounding the various conductors in the field. The first thing, 
therefore, that we have to do is to see whether experiment throws any 
light on this point. 

When a dielectric is in an electric field it experiences a change in its 
structure ; this is rendered evident by the alterations in its volume and 
elasticity observed by Quincke, by the change in its optical properties 



\ 



ON ELECTKICAL THEORIES 143 

observed by Kerr, and also by the fracture of the dielectric when the 
field is made sufiBciently intense. So that whenever an electromotive force 
acts on a dielectric it produces a change in its structure which we shall 
always speak of as polarisation. This, strictly speaking, has only been 
directly proved for electromotive forces produced by charges of statical 
electricity ; but, unless we are prepared to say that the electromotive 
force due to statical electricity is in some way different from that due to 
a changing current, we must admit that when an electromotive force of 
the latter kind acts on a dielectric it polarises it. And we are not with- 
out experimental evidence that the electromotive force due to variations 
in the vector potential does produce some of the effects of the electromo- 
tive force due to a charge of statical electricity. Rowland's experi- 
ments have shown that a moving electrified body will set a magnet 
placed near to it in motion. It follows from this, by dynamical prin- 
ciples, that if we have the charged body initially at rest and move the 
magnet it will, if no other forces act upon it, be set in motion ; so that 
in this case there is an electromotive force due to the motion of the 
magnet, i.e., the variation in the vector potential produces the same 
effect on the electrified body as the electromotive force due to a charge of 
statical electricity. For this reason we shall suppose that the electro- 
motive force due to the variation in the vector potential always produces 
effects on a dielectric on which it acts of the same type as those which 
have been observed to arise from the action of an electromotive force due 
to a charge of statical electricity. 

Let us now consider a magnet surrounded by a dielectric. If we set 
the magnet in motion, we produce an electromotive force which polarises 
the dielectric. Let us, to fix our ideas, consider an element of the dielec- 
tric and the magnet. When the magnet moves it polarises the dielectric ; 
it follows from dynamical principles (an extension of the principle of 
action and reaction),' that if the polarisation of the dielectric be 
altered, the magnet will move, so that a change in the polarisation of a 
dielectric produces a magnetic force. 

Again, let us instead of the magnet consider a coil of wire conveying 
a current. A change in the rate of flow of the current produces a 
change in the polarisation of the dielectric ; it follows that a change in 
the rate of change of the polarisation of the dielectric will produce a 
change in the current, i.e., will produce an electromotive force. 

It follows too, from dynamical principles, that as the change in the 
polarisation of an element of the dielectric due to the change in the 
current depends on the distance of the element from the current, there 
must be a force between the current and the element when the polari- 
sation of the latter is changing. Thus we see that a change in the 
polarisation of the dielectric must produce all the effects of an ordinary 
conduction current, so that it is only absolutely necessary to consider 
how the experimental evidence affects those theories which take the 
action of the dielectric into account. As, however, the experiments 
which have been made are few in number, and are all concerned with 
interesting points, we shall consider them in their relation to all the 
theories, and not only to those which take the dielectric into account. 

' See a paper by the author of this report ' On some Applications of Dynamical 
Principles to Physical Phenomena,' P/dl. Trans., 1885. 



144 EEPORT — 1885. 

Schiller's Experiments. 

The first experiment whicli we shall discuss is oue made by Schiller^ 
and described by him in Poggendorf s Annalen, vol. clix. pp. 456, 537 j 
it was intended to test the potential theories of Neumann and Helm- 
holtz. We saw that, according to these theories, in an unclosed circuit 
there are, in addition to the forces due to the elements of current, and 
which are expressed by Ampere's law, forces arising from the discon- 
tinuity of the currents at the ends of the circuit. If we have an end of a 
circuit where the current stops, and the electricity accumulates at the 
rate dejdt, it will exert on an element of current of length ds traversed 
by a current of intensity i a force tending to the end and equal to 

i 2 • 7 de cos Q 

* * 'Jt ^r 

where is the angle between the element of current and the radius drawn 
to it from the end. If we calculate from this expression the couple pro- 
duced by an end on an endless solenoid, or on what is practically the 
same thing, a ring magnet, we shall find that the couple tending to turn 
the ring about an axis in its own place will not vanish, while the couple 
arising from the forces given by Ampere's law will. Thus if the ring 
rotates, as it should according to the potential theory, it must be from 
the action of the end. 

In Schiller's experiment the end of the current was the end of wire 
connected with a Holtz machine. This was placed near to a ring magnet 
which was suspended by a long cocoon fibre ; the magnet was protected 
from electrostatic influences by being enclosed in a metal box connected 
with the earth. Schiller determined the intensity of magnetisation of 
the ring magnet and the quantity of electricity passing through the 
point, and he calculated that if the potential theory were true, he ought 
to get a deflection of the magnet of about 27 scale divisions, instead of 
which there was no perceptible deflection. 

This experiment shows conclusively that the potential theory is wrong 
if we neglect altogether the action of the dielectric, and assume the cur- 
rent to stop at the end of the wire. If, however, we take the dielectric 
into account, the experiment tells us nothing as to whether Maxwell's 
theory or the more general one is true ; for since the current from the 
Holtz machine is steady, as much electricity flows out from the end of 
the wii'es as arrives there ; and thus there is really no discontinuity in 
the current, the only difference being that before reaching the end the 
current is flowing through copper and after passing it through air. The 
condition of things at the end of the wire remains steady, and thus the 
quantities which we denoted by P and 2 vanish. 

The experiment might, however, be modified so as to be capable of 
distinguishing between the theories which take the dielectric into account, 
For suppose that, instead of letting the electricity escape through the 
point, we never let the potential at the end of the wire get so high as to 
allow the electricity to escape ; then if the wire is initially uncharged, the 
condition at the end will be changing whilst the wire is charging up, and 
thus 2 will have a finite value ; so that if the magnet were sufficiently 
delicate and remained undeflected, whilst the point was surrounded by 
dielectrics of all kinds, it would show that Maxwell's theory is correct. 

I have calculated the effect which would be produced on Schiller's 



ON ELECTRICAL THEORIES. 145 

suspended magnet, and find that it is too small to be observed ; as, bow- 
ever, the time of charging up the wire will be very small compared with 
the time of vibration of the magnet, the effect will be of the nature of an 
impulse, so that in this case there will be considerable advantage in 
having the moment of inertia of the suspended magnet small ; while, 
as Schiller arranged the experiment, there was no such advantage, as the 
thing expected was a steady deflection. Thus if the ring magnet were 
retained it would be desirable to make the opening of it as small as pos- 
sible, retaining the same cross action. I think the arrangement could 
be made sensitive enough to be deflected if the value of S were any 
considerable fraction of the rate of increase of the electricity at the end 
of the wire. 

There is another way in which the continuity or discontinuity of the 
current might be tested, and which might perhaps be more delicate than 
the last. We saw on p. 141 that at any point of a current at which S 
had a finite value the mechanical force on the element is not at right 
angles to the element. In addition to the ordinary force at right angles 
to the element, there is a force in the direction of the vector potential 
equal in magnitude to the product of the values of the vector potential 
and 2. 

The existence of this force could be tested 
by an arrangement of the following kind : — 

AB and CD are light movable segments 
of the same circle, having balls covered with 
paraifin A, B, C, D fastened to their ends. 
These segments are connected with a very light 
framework which can rotate about an axis per- 
pendicular to the plane of the segments ; the 
segments touch at their middle points contact, 
pieces which are connected with a Holtz ma- 
chine. EP is the section of an electromagnet 
concentric with AB and CD ; the whole is surrounded with a metal 
cylinder to screen it from external electric influences. When a curi'ent 
is passing through the electromagnet it produces a vector potential, 
whose direction is at right angles to the radius from O, the centre of the 
electromagnet perpendicular to its axis. Thus if 2 exists there will be a 
couple tending to twist the system AB, CD about its axis, but if S exists 
at all it will be when the electrical condition of the balls A, B, C, D is 
changing, so that unless the currents are continuous we should expect the 
system to rotate when the balls are being charged up. I have calculated 
that the system might easily be made sensitive enough to be sensibly 
deflected on charging or discharging, pi'ovided 2 is an appreciable fraction 
of the rate of change of the surface-density of the electricity on the balls. 

Schiller's Secojid Experiment.^ 

Schiller has made another experiment, which shows that Ampere's 
theory fails for unclosed circuits. The first form of the experiment con- 
sisted in having a solenoid placed over a condenser one of whose plates 
could rotate about a vertical axis coinciding with the axis of the solenoid. 
One end of the solenoid was connected to one plate of the condenser and 
the other end to the other plate. When the solenoid is connected to a 

' Pogg. Ann., clix. p. 456; clx. p. 333. 

1885. L 




146 KEPOET— 1885. 

battery the condenser will charge up and there will be radial currents of 
electricity in the plates ; the current passing through the solenoid will 
produce a magnetic force which will, if Ampere's theory be true, act on 
the radial currents in the plate of the condenser and set it in rotation. 
Schiller found that this effect was too small to be observed, so he modi- 
fied the experiment in the following way. Let us suppose that we have 
the two plates of the condenser rigidly attached to their axis and placed 
in a field symmetrical about its axis, in which the vertical component 
of the magnetic force is not uniform. Then if a current be sent through 
the upper plate, down through the axis, and out at the lower plate, the 
couple tending to twist the lower plate will not be equal and opposite to 
that tending to twist the upper one, as the magnetic force is not equal at 
the two plates, and thus the condenser will be set in rotation. Con- 
versely, if the condenser be set in rotation in the magnetic field, and two 
electrodes of a galvanometer be connected with its axis, then if Ampere's 
theory be trne there will be an electromotive force acting round the 
galvanometer circuit, which will produce a current, and this current 
could be much more easily detected than the rotation in the first form of 
the experiment. Schiller calculated the deflection which he ought to get 
if Ampere's theory were true, and found that he could easily detect it if 
it existed ; as he was not able to see any deflection, we must conclude 
that Ampere's theory is not the true one. 

It is easy to see that, according to the potential theory, there would 
be no curreutin the galvanometer ; for, as everything is symmetrical about 
the axis, the potential is not altered by the rotation. The following 
calculation will show that, according to the dielectric theories, there should 
be no current through the galvanometer. 

For if a, b, c are the components of magnetic induction, F, G, H 
those of the vector potential, X, Y, Z those of the electromotive force, 
then 



dt clt dx \ dt dt dt J 

„ dz dx d ^ -rj, dx p dy , -ri clz\ 

^ = "^1- ' dt'dyV It-^ ^ '^dt''^ dt] 



i 



Suppose the condenser is rotating with an angular velocity w about 
the axis of Z ; then the E.M.F. arising from one plate is, if E, be its radius, 



'^0 



-'-(^-S+«t)- 



Now F ^ -h G I' = ..Re, 

dt at 

where is the component of the vector potential along the direction 
of motion of a point on the circumference of the plate of the condenser. 

But the line integral of the vector potential round any curve equals 
the number of lines of magnetic force passing through it, so that, since 
the field is symmetrical, 

.R 
27r cr dr = 27rRe. 



ON ELECTRICAL THEORIES. 



147 



From this equation we see that the E.M.F. due to the rotation vanishes 
for each plate, so that, according to this theory, there should be no current 
through the galvanometer. 

This experiment of Schiller shows that both Grassmann's and Clau- 
sius' theories must be wrong, as well as Ampere's and Korteweg's, for 
we can easily see that they would make the disc rotate in the way in 
which Schiller first tried the experiment, and if this were so, it follows 
from dynamical principles that a current must be produced in the second 
form of the experiment. 

This would seem to be the case even if we take into account the cur- 
rents in the dielectric, unless we suppose that all the circuits are closed, 
for if all the circuits are closed then the disc will not rotate, as all the 
theories agree. If the circuits are not closed we may divide the currents 
in the disc into two parts, one part being of such magnitude as to form 
with the dielectric currents closed circuits ; then the forces on this part 
and the dielectric will form a system in equilibrium ; and there remains 
the other part of the currents, the action of the magnet on which ought to 
set the disc in rotation. Taking Schiller's experiments together, we may 
say that they show that the dielectric must be taken into account, and 
that some form of the potential theory is the only one of the theories we 
are considering which can give the expression for the forces due to a 
distribution of currents. 

Although these two experiments of Schiller's show that of the 
theoi'ies we have discussed only the dielecti'ic ones can be retained, we 
shall describe one or two more experiments which have been or could be 
made to distinguish between the various theories. Clausius' and Grass- 
mann's theories lead to the same expression for the force between two 
elements of current, so that these theories stand or fall together. Grass- 
mann in his paper ^ describes an experiment which would distinguish 
between his theory and Ampere's, or, in fact, any other except Clausius' 
which has ever been published. 

Suppose that NS and SN" are two mag- 
nets whose north and south poles are de- 
noted by N and S respectively, and that 
these magnets are fastened together by a 
rod NS, the system being suspended by a 
cocoon thread attached to the middle point 
of NS. Let AB be an unclosed circuit, say 
a wire joining the plates of a charged con- 
denser ; then, according to Grassmann's and 
Clausius' theories, the system will rotate in 
such a way that the sense of rotation is re- 
lated to a vertical line drawn downwards 
like rotation and translation in a right- 
handed screw. According to every other theory it will rotate in the 
opposite direction. 

Another experiment has iDeen made by v. Helmhoitz,^ which shows 
that the potential theory leads to wrong results unless the action of the 
dielectric is taken into account, hh is a rotating conductor, to the ends 
of which large condenser plates are attached, which, when in rotation, 
come very near to the similar plates c, c. The plates h and c are segments 



s 



N 



Pogg., Ixiv. 1, 1845. 



WissensohaftlicJie Ahhandhmgen, vol. 



783. 
L2 



148 



EEPOKT — 1885. 



of coaxial cylinders. lu v. Helmholtz's experiments bh was rotated 
between the poles of a powerful electromagnet. The plates c, c were 
connected with a commutator, which put them to earth when the rotating 
piece was in the position A, and to the plates of a Kohlrausch condenser 
when it was in the position B. Now suppose there is a difference of 
potential between h and c ; suppose, for clearuess, that 6 is at a higher 
potential than c, then when the rotating piece is in the position A the 
positive electricity goes to earth, and the negative is left to go to the 
Kohlrausch condenser, when the rotating piece gets to the position B. 
The change in this condenser was measured by a quadrant electrometer. 
V. Helmholtz found that the needle of the electrometer was deflected when 
the piece hh was rotating. Since everything is symmetrical about the 
axis of rotation, there would be no difference of potential between the 






plates h and c, according to the potential law, if we neglect the action of 
the dielectric. According to Ampere's law there will be a difference of 
potential between h and c equal to Qmo, whei'e a is the radius of the rotat- 
ing piece, w its angular velocity, and 9 the vector potential along the 
direction of motion of the disc. According to the dielectric theory there 
will also be the same difference of potential between h and c if we sup. 
pose that there is no discontinuity in tbe motion. We shall suppose that, 
instead of the velocity changing abruptly from (oa to zero as we pass 
from the rotating conductor to the dielectric, there is a layer of the 
dielectric next to the conductor in which the change of velocity is very 
rapid, one side of the layer moving' with the velocity wa, the other side 
being at rest. Then, using the same notation as before, we have — 

'—. '^1/ -h'k. __ . — , ^ 

(It dx\" clt ' ^ dt ' " dt 



X=c 



dt dy L 



dt 



dz 



dx q(7^/ 
dt dt 



+ H 



dt 



} 



I 



Integrating across the thin layer of the dielectric, in which the velocity 
is changing rapidly, we see that the difference of jDotential between b 
and c equals 



where dxjdt, dijjdt, dzjdt are the velocities of a point on the boundary 



ON ELECTRICAL THEOEIES. 149 

of the moving conductor. This equals Qaw, the same value as that 
given by Ampere's theory, so that in this case the two theories lead to 
identical results, which are in agreement with the result of Helmholtz's 
experiments. 

Rontgen has recently published ' a preliminary account of some 
experiments which seem to pi'ove directly that the variations in the 
dielectric polarisation produce eflPects analogous to those due to a 
current. 

This completes the account of the experiments which have been made 
to test the various theories. As the result of them we may say that they 
show that it is necessary to take into account the action of the dielectric, 
but they tell us nothing as to whether any special form of the dielectric 
theory, such as Maxwell's or Helmholtz's, is true or not. 

I have described two experiments which would decide whether 
Maxwell's theory that all circuits are closed is true or not. It seems to 
me, however, that even if Maxwell's theory be wrong, Helmholtz's is not 
the only alternative. I have given a sketch of a theory in which I have 
tried to make as few assumptions as possible ; all that I have assumed is 
that when a dielectric is acted on by a changing electromotive force, 
it behaves like a conductor conveying a current whose intensity is pro- 
portional to the rate of change of the electromotive force. We know 
from experiment that it produces effects of the same character, and I 
have assumed as the simplest assumption I could make that for the same 
dielectric the equivalent current is proportional to the rate of change of 
the electromotive force, so that equivalent current = r/ (rate of change 
of electromotive force). 

Both Maxwell and Helmholtz assume that rj depends only on the 
specific inductive capacity of the dielectric, but I think it is preferable, 
until we have more experiments on this point, to look on r) as the measure 
of a new property of a dielectric, and not to assume that it is merely a 
function of the specific inductive capacity, the only experimental evi- 
dence for this being the by no means perfect agreement between the refrac- 
tive index and the reciprocal of the square root of the specific inductive 
capacity. To prove Maxwell's theory of closed circuits it would not be 
sufiicient to prove that for one medium, say air, r; =::■ K/47i-, for it is quite 
conceivable that electrical phenomena may be simpler in a dielectric like 
air, where the electrical behaviour of the ether seems to be but little 
affected by the presence of the dielectric, than in such a one as glass or 
other substance possessing a comparatively large specific inductive 
capacity, when the effect of the ether is seriously modified by the 
presence of the medium. 

Since in the theory I have sketched the values of 

du d V dvj 
dx dy dz 
and I (it, — ^(2) + in (u, — v^) + n (wj — iv^) 

are not zero, but arbitrary, inasmuch as they involve ?;, in order to find 
the value of the force between two circuits where there is any dis- 
continuity in the currents we shall require to know the value of the 
quantity k which occurs in v. Helmholtz's theory. 

The most pressing need in the theory of electrodynamics seems to 

' Phil. Mag., May. 1885. 



150 EEPOET — 1885. 

be an experimental investigation of the question of the continuity of tliese 
dielectric currents ; we have experimental proof that they exist, but we 
do not know whether Maxwell's assumption that they always form closed 
circuits with the other cui'rents is true or not. If Maxwell's assumption 
should turn out to be true, we should have a complete theory of electrical 
action ; if, on the other hand, it should turn out to be wrong, then we 
should have to go on to determine the quantity h. This quantity is diffi- 
cult to determine, as its influence on all closed circuits disappears. It 
influences, as v. Helmholtz has shown, the rate of propagation of the 
electric potential along conducting wires, and I think we can see that it 
would influence the time of oscillation of an irregular distinbntion of elec- 
tricity over a conducting shell. The easiest way, however, of determin- 
ing this quantity would seem to be the straightforward one of measuring 
electrostatically the value of the electromotive force due to a valuation 
in the charge of a condenser ; the expression for the vector potential, as 
we saw on p. 140, involves h, so that if we measure the electromotive 
force, which is equal to the i-ate of variation of the vector potential, we 
shall determine the value of the vector potential, and consequently of Ic. 



Appendix I. 

Since the Report was written I have had through the kindness of the 
author an opportunity of seeing the advance proofs of a paper by Pro- 
fessor J. H. Poynting, of Mason's College, Birmingham, ' On the Connexion 
between Electric Current and the Electric and Magnetic Induction in 
the Surrounding Medium,' which is about to appear in the ' Philosophical 
Transactions.' 

The views expressed in this paper are rather a new way of looking at 
Faraday and Maxwell's theory than a new theory of electrodynamio 
action, as however it brings the action of the dielectric into great 
prominence it is instructive to consider it. 

The paper is largely based on a previous one by the same author on 
the ' Transference of Energy in the Electromagnetic Field,'' it is therefore 
necessary to give a brief account of this paper. 

In it the author shows that the rate of increase of the energy inside 
any closed surface equals 

^{[{l (R'/5 - Q'y) + m (yF - aW) + n («Q' - /3F)}c?S, 

where cZS is an element of surface, 1, m, n the direction cosine of the 
normal to JS, o, /3, y the components of magnetic induction, and 
P', Q', R' given by the following equations : — 

p,^_dF_# 

dt dx* 

^ -" dt dif 

cm chj. 

^ ~ dt dz' 
' Phil. Trans., 1884, part ii 



ON ELECTBICAL THEORIES. 151 

■where r, G, and H are the components of the vector potential and xp ^^^ 
electrostatic potential ; thus if the medium is at rest P', Q', H' are the 
components of the electromotive force at the point. 

Professor Poynting interprets this equation to mean that the components 
parallel to the axes of x, y, z of the flow of energy across each element of 
surface are respectively 

2:(R'^-Q-V), 

4ir 

1 (Q'« - ?'/3), 

so that according to this view the energy flows in the direction which is 
at right angles both to the magnetic and electromotive forces, and in the 
direction in which a right-handed screw would move if turned round 
from the positive direction of the electric intensity to the positive 
direction of the magnetic intensity ; the quantity of energy crossing in 
unit time unit surface at right angles to this direction being 

— . Electromotive force at the point X magnetic force 

X sine of the angle between these forces. 

This interpretation of the expression for the variation in the energy seems 
open to question. In the fir.st place it would seem impossible a priori to 
determine the way in which the energy flows from one part of the field 
to another by merely differentiating a general expression for the energy 
ill any region with respect to the time, without having any knowledge of 
the mechanism which produces the phenomena which occur in the 
electromagnetic field : for although we can by means of Hamilton's or 
Lagrange's equations deduce from the expression for the energy the 
forces present in any dynamical system, and therefore the way in which 
tlie energy will move, yet for this purpose we require the energy to be 
expressed in terms of coordinates fixing the system, and it will not do to 
take any expression which happens to be equal to it. The problem 
of finding the way in which the energy is transmitted in a system whose 
mechanism is unknown seems to be an indeterminate one ; thus, for 
example, if the energy inside a closed surface remains constant we cannot 
unless we know the mechanism of the system tell whether this is because 
there is no flow of energy either into or out of the surface, or because as 
much flows in as flows out. The reason for this diff'erence between what 
we should expect and the result obtained in this paper is not far to seek. 
Though tlie increase in the energy inside a closed surface equals 



i||{KR'/3-Q'r) + . • • -l^S, 



it does not follow that the components of the flow of energy across each 
element of surface are (R'/j — Q'y)/^'!', &c., for we can find quantities 
u, V, IV which are of the dimensions of rate of change of energy per unit 
area, and for which 

(lu + mv + niv) dS := 0. 



u ■ 



152 EEPORT — 1885. 

The following values of u, v, iv satisfy this condition : — 
= 1 / JL. (FG) - -^ (HF) \ , 

t, = i ( JlL^ (GH) - -^ (FG) 1 , 

w = ^( /^' (HF) - f\ (GH) ], 
fj.ldx dt ^ ^ dijdt^ ^ r 

where /x is the magnetic permeability and F, G, H are the components 
of the vector potential, or if i// be the electrostatic potential 

«=^{#hJ-,^{^^g1, 

dy L dz J dz [. dy J 



dy L dz J dz {. dy 

. = ^(l^FJ-^(i^Hl, 
dz L dx i dx I dz J 

^„=i.(^G"i-^{^^p"l, 

(/a; L t'y J dy [. dx J 



If the values of u, v, w which satisfy these conditions be denoted by 
the («!, ^1, w{), {u^, V2, w^ . . . then the flow across any element of 
surface might have for its x component — 

~(R' ft - Q' y) + Xi «, + Xo u, + \3 % + . . . 

where X,, Xj, X^ are arbitrary constants, thus we see that the components 
of the flow of energy, instead of being uniquely determined by this pro- 
cess are really left quite indeterminate by it. Though this is so, it is very 
instructive to follow Professor Poynting's description of the way in which 
the energy flows in some special cases ; we shall select a very simple one, 
the case of a current flowing along a straight wire. Here the lines of 
electromotive force are straight lines parallel to the wire, the lines of 
magnetic force are circles with their centres on the wire, and their planes 
at right angles to it. Then, since according to the view expressed in 
the paper, the energy moves at right angles both to the electric and 
magnetic forces, it must in this case move radially inwards to the wire 
where it is converted into heat. The energy, instead of being supposed 
to be transmitted through the wire, is regarded as transmitted by the 
dielectric ; and though we may not regard the exact law of flow of 
the energy as established, still it is very important that this view 
should be brought into prominence. Another important point brought 
prominently forward in this paper is the view that magnetic force is 
always the sign of transference of energy, according to Professor 
Poynting ; indeed, there must be transference of energy from one part of 
the field to another to give rise to magnetic force. Thus, according to 
his view, no magnetic force would be exerted by the discharge of a leaky 
condenser, because in this case he considers the energy to be confined to 
the space between the plates of the condenser and to be converted into 
heat where it stands. If the plates were connected by a metallic wire, 
the energy could flow out and be converted into heat in the wire and 
this motion of energy would give rise to magnetic forces, so that magnetic 



ON ELECTRICAL THEOEIES, 153 

forces wonldbe produced by the discharge of a condenser in this way, but not 
by leakage. In this case the theory differs from Maxwell's, as according 
to that theory the alteration in the electromotive force w,ould produce 
magnetic forces in either case. 

In Professor Poynting's second paper, which we have already men- 
tioned, the fundamental principles of electrodynamics are described as 
the results of the motion of the tubes of electromotive and magnetic 
force. Maxwell develops electrodynamics from the principles : — 

1st. That the total electromotive force round any closed curve is 
equal to the rate of decrease of the total magnetic induction through the 
curve. 

2nd. The line integral of the magnetic force round any closed curve 
is equal to 4:ir times the current through the curve. 

Professor Poynting restates these principles in the following way : — 

1. ' Whenever electromotive force is produced by change in the mag- 
netic field, or by motion of matter through the field, the E.M.P. per 
unit length is equal to the number of tubes of magnetic induction 
cutting or cut by the unit length per second, the E.M.P tending to 
produce induction in the direction in which a right-handed screw would 
move if turned round from the direction of motion relatively to the tubes 
towards the direction of the magnetic induction.' 

The second principle he states in the following way : — 

' Whenever magnetomotive force is produced by change in the electric 
field, or by motion of matter through the field, the magnetomotive force 
per unit length is equal to 47r times the number of tubes of electric 
induction cutting or cut by unit length per second, the magnetomotive 
force tending to produce induction in the direction in which a right- 
handed screw would move if turned round from the direction of the 
electric induction towards the direction of motion of the unit length 
relatively to the tubes of induction.' 

By magnetomotive force is meant the line integral of the magneto- 
motive force round a tube of induction. This statement includes the 
more special one that the line integral of the magnetic force round any 
closed curve is equal to 4m times the number of tubes passing in or out 
through the curve per second. 

The development of these principles leads to equations which are 
practically the same as those obtained by Maxwell, the chief difference 
being that the quantity corresponding to Maxwell's J is no longer 
arbitrary or rather redundant. 

Professor Poynting also introduces into his equations the time 
integrals of the components of the magnetic force as fundamental quan- 
tities, and regards the components of the magnetic as the differential 
coefficients of these quantities with regard to the time. This method of 
representing magnetic force was also used by Professor Fitzgerald in his 
paper on the Electromagnetic Tlieory of the Reflection and Refi-action 
of Light.' It has the advantage of calling attention to the dynamic 
character of magnetic phenomena. In Professor Poynting's paper some 
of the applications of his method of regarding electrical phenomena are 
worked out with great detail for some of the simpler cases. 

■ PMl. Trans., 1880, part ii. 



1<'54 EEPOET — 1885. 

Appendix II. 

ON THE STRESS IN THE DIELECTRIC. 

In the preceding Report we have had so frequently to refer to the 
action of the dielectric that it may be convenient to give a very brief ac- 
count of the work which has been done on the stresses which are sujDposed 
to exist in it. We shall confine ourselves to the work which has been 
done on the stresses in the electrostatic field; those existing in the electro- 
magnetic field are of a similar nature, so that any remark applying to 
one will also apply to the other. The idea of explaining the forces 
in the electrostatic field by means of stresses in the dielectric seems to be 
due to Faraday, who describes ' the stress in the medium by sayiug that 
the lines of force tend to contract and also to repel one another. The 
magnitude and distribution of this stress was investigated by Maxwell ; ^ 
he found that in a medium whose specific inductive capacity was K, and 
at a point where the electromotive force is E, a tension equal to KR^/Btt 
per unit area along the lines of force combined with a pressure of the 
same amount at right angles to these, would produce the effects observed 
in the electrostatic field, that is, at a point in a dielectric, the resultant of 
these stresses would be a force whose components, parallel to the axes of 
X, y, z, are eX, eY, eZ respectively, e being the charge of electricity at the 
point, and X, Y, Z the components of the electromotive force. It may be 
observed that this system of stress could not be produced by the strain 
in an elastic solid at rest : this points to the kinetic origin of "electrostatic 
phenomena. 

These stresses are in equilibrium at a point in a dielectric where there 
is no free electricity. At the junction of two media, whose specific inductive 
capacities are K, and Kg, and in which the electromotive forces are 
Ri and Rj, and whose interface is perpendicular to the lines of forces, 
the stresses are not in equilibrium, but there is an unbalanced stress 
(Kj Ri" — Ko Rj-) /Stt which will tend to make the boundary move 
towards the medium whose specific inductive capacity is Kj ; if these 
dielecti'ies are liquids, their interface may become curved so that the forces 
due to surface tension balance this stress. 

Quincke,^ who has experimentally investigated the effects of electrifi- 
cation on various dielectrics, such, for example, as the efiects on the glass 
of a Leyden jar, has found that the efi'ects on difi^erent bodies ai-e very 
different ; he finds, for example, that though the effect of the electrification 
on the dielectric of the Leyden jar is generally to produce an expansion, 
yet^ in some substances, such as the fatty oils, contraction takes place.* 
This diversity in the effects of electrification on different dielectincs shows 
that the distribution of stress cannot be so simple as was supposed by 
Maxwell. It also shows that there must be forces in the electric field 
which are not recognised either by Maxwell's theory or the theory of 
action at a distance. More general theories have been given in order to 
meet this difficnlty. 

' ExjjeTiiHeiital Eesearchcs, § 1 297. 
^ Wectrioity and Magnetism, 2ncl edition, p. 149. 

3 Wiecl. Ann., x. pp. l(jl, 374, 513; IMd., ix. p. 105; Pidl. Mag., yo\.:^. n. ZO 
(1880). I ' J ' I 

* The fatty oils are also an exception to the rule that the index of refraction 
equals the square root of the specific inductive capacity. 



ON ELECTEICAL THKOEIES. 155 

T. Helmholtz ' lias supposed tliat a change in the density of a dielec- 
tric might alter its specific inductive capacity, and he has investigated 
the consequences of this supposition. Korteweg and Lorberg ^ have 
investigated the more general case, when the specific inductive capacity 
of a strained dielectric is supposed to be a function of the strains. 
Korteweg supposes that if the body suffers dilatation e along the lines of 
force, and dilatations / and cj at right angles to them, then the specific 
inductive capacity = K— ae— /3 {f+g)- Helmholtz assumed that 
a = /3. The presence of strain in a dielectric must influence the specific 
indiTctive capacity, for Quincke has shown that the various coefficients of 
elasticity are altered under the influence of electricity. Lorberg, I.e., has 
found the distribution of stress in the medium when the specific inductive 
capacity alters in this way. He finds that there is a tension along the 
line of force equal to 



and a pressure at right angles to them equal to 

KStt 2 J 
The force in the medium parallel to the axis of x 



where 

*±7r tCit/ tltl/ tviO tltt' tvU tlAf till 

+ _^ (a-/3) ^^ 
dz dx dz 

Where is the potential, and p the volume density of the free electricity. 
The part A of this force exists even when there is no free electricity at 
the place under consideration ; if the dielectric were a fluid, these terms 
would indicate forces tending to move the fluid when placed in a variable 
electx'ic field ; this motion, however, seems not to have been observed. 
The supposition made by Korteweg and Lorberg is not the most general 
one that could be made ; we might assume that the specific inductive 
capacity of the strained body became difl'erent in different directions, So 
that the body would behave like a crystal. Dr. Kerr's experiments on 
the double refraction in liquids placed between the poles of a powerful 
electrical machine seem to point to this conclusion. 

Kirchhoff ^ has made similar assumptions to those of Korteweg and 
Lorberg on the effect of strain on the specific inductive capacity, and has 
arrived at similar equations ; in the second paper he applies these equations 
to some cases which Quincke investigated experimentally. 

' V. Helmholtz, Wied. Ann., xiii. p. 385; WissenscJiaftl. Abh. vol. i. p. 298. 
^ Korteweg, Wied. Ann., ix. p. 48 ; Lorberg, Wied. Ann., xxi. p. 300. 
' Wied. Ann., xxiv. p. 52, 1885 ; Ibid., xxv. p. 601, 1885. 



156 EEPOET— 1885. 



Second Report of the Committee, consisting of Professor Schuster 
(Secretary), Professor Balfour Stewart, Professor Stokes, Mr. 
Gr. Johnstone Stoney, Professor Sir H. E. Eoscoe, Captain 
Abney, mid Mr. Gr. J. Symons, appointed for the purpjose of 
considering the best methods of recording the direct intensity of 
Solar Radiation. 

The Committee, working on tlie lines of their last report, have given their 
attention to the best form of a self-recording actinometer, and have come 
to the following conclusions : — 

1. It seems desirable to construct an instrument which would be a 
modification of Professor Stewart's actinometer adapted for self-registra- 
tion — the quantity to be observed being, not the rise of temperature of 
the inclosed thermometer after exposure for a given time, but the excess 
of its temperature when continuously exposed over the temperature of the 
envelope. 

2. As the grant to the Committee will not admit of the purchase of 
a heliostat, it will no doubt be possible to procure the loan of such an 
instrument, and, by making by its means sufficiently numerous com- 
parisons of the instrument proposed by the Committee with an ordinary 
actinometer, to find whether the arrangement suggested by the Committee 
is likely to succeed in practice. The Committee would therefore confine 
their action for the present to the carrying out of such a series of 
comparisons. 

3. The size of the instrument might be the same as that of Professor 
Stewart's actinometer. 

4. The instrument should have a thick metallic enclosure, as in the 
actinometer above mentioned, and in this enclosure there should be 
inserted a thermometer to record its temperature. Great pains should 
therefore be taken to construct this enclosure so that its temperature shall 
be the same throughout. 

5. The interior thermometer should be so constructed as to be readily 
susceptible of solar influences. It is proposed to make it of dark glass, 
of such kind as to be a good absorber, and to give it a flattened surface 
in the direction perpendicular to the light from the hole. 

6. It seems desirable to concentrate the sun's light by means of a 
lens upon the interior thermometer, as in the ordinary instrument. For 
if there were no lens the hole would require to be large, and it would be 
more difficult to prevent the heat from the sky around the sun from 
interfering with the determination. Again, with a lens there would be 
great facility in adjusting the amount of heat to be received by employing 
a set of diaphragms. There are thus considerable advantages in a lens, 
and there does not appear to be any objection to its use. 

The Committee have not drawn their grant (201.). They suggest 
that they be reappointed, and that the unexpended sum of 20?. be again 
placed at their disposal. 



ON OPTICAL THEORIES. 157 



Report on Optical Theories. 
By E. T. G-LAZEBROOK, M.A., F.R.S. 

Dk. Lloyd's well-known Report on Physical Optics was presented to the 
Association at its meeting in Dublin in 1834 — fifty-one years ago. Since 
that time the question of double refraction has been treated of very fully 
by Professor Stokes in the Report for 1862, but unfortunately he con- 
fined himself to that one branch of the subject. The years immediately 
succeeding that in which Dr. Lloyd's report was read were mai'ked by 
work of great importance, which has formed the basis for much that has 
since been done, and it is necessary, before writing of recent progress in 
the subject, to consider somewhat carefully the researches o£ Green, 
MacCullagh, Cauchy, and F. Neumann. 

This 1 propose to do, in as brief a manner as possible, for that part of 
the subject which is not included in Professor Stokes's report. I then 
propose to go on to the consideration of more modern work, treating sepa- 
rately (1) of the simple elastic solid theory, (2) of theories based on 
the mutual reactions of matter and ether, (3) of the electro-magnetic 
theory. 

PaKT I. — IXTRODUCTION. 
THE WORK OF MACCULLAGH, KEUMANy, GREEN, AND CAUCHY. 

Chapter I. — MacCullagh. 

§ 1. Fresnel ' himself had developed a theory of reflexion and re- 
fraction, and had arrived at formulas giving the intensities of the reflected 
and refracted waves in terms of the incident. 

In obtaining these he relied on the two following principles : — 

The resolved parts of the displacements parallel to the face of inci- 
dence are the same in the two media. 

The total energy in the reflected and refracted waves is equal to that 
in the incident wave. 

He further supposed that the rigidity of the ether is the same in all 
transparent media, and hence that reflexion and refraction are produced 
by a change of density ; from this it follows that the refractive index of 
a medium is proportional to the square of the density of the ether in the 
medium. The direction of vibration is considered to be perpendicular to 
the plane of polarisation. According to this theory there is a discon- 
tinuity in the component of the vibration at right angles ^ to the surface. 

§ 2. An elegant geometrical expression of the laws to which these 
principles lead was given by MacCullagh. He defines as the trans- 
versal of a ray the line of intersection of the wave front and the 
plane of polarisation ; the length of this line being proportional to the 

' Fresnel, Ann. dc Chlm. et do Physique, t. xlvi. p. 225 ; (Eiivres completes, 
t. i. p. 767. 

^ For a further consideration of this point see p. 186. 



158 EEPOBT — 1885. 

amplitude of the vibration multiplied by tbe density of tlie medium. 
Then Fresnel's results may be expressed by the statement that the trans- 
versal of the incident ray is the resultant, in the mechanical sense of the 
word, of those of the reflected and refracted rays. 

This first suggestion of MacCullagh's was modified by reading some 
of Cauchy's work on double refraction, from which it appeared possible 
that the vibrations of polarised light might lie in the plane of polarisa- 
tion instead of at right angles to it. Adopting, then, this hypothesis, 
a transversal represents in addition the direction of vibration ; and if the 
further supposition is made that the ether is of the same density in all 
media, so that reflexion and refraction arise from variations in its 
rigidity and not in its density, expressions very nearly identical with 
Fresnel's can be found for the intensities of the reflected and refracted 
rays, while at the same time the principle of the continuity of the 
displacement normal to the surface is satisfied. 

§ 3. These three principles — 

(1) The ether is of the same density in all media, 

(2) The displacement is the same on both sides of the surface of 
separation of the two media, 

(3) The energy of the incident wave is equal to that of the reflected 
and refracted waves 

— were applied by MacCullagh to the problem of reflexion and refrac- 
tion at the surface of a crystal, and the results of a first investigation 
were communicated to the meeting of the Association in 1834. 

The theory as there given was somewhat modified in consequence of a, 
paper by Seebeck in Poggendorif 's ' Annaleu,' and took its final form in 
a memoir read before the Irish Academy ' in January 1837. MacCuUao-h 
in this paper states his fundamental principles, not as based on mechanics, 
but merely as those which had led him to a solution, the results of 
which agree closely with the experiments of Seebeck and Brewster. 

The analysis of the problem is greatly simplified by the introduction 
of the idea of ' uniradial directions.' 

In a crystal, for any given direction of incidence, there are two posi- 
tions for the incident transversals, which give rise each to only one 
refracted ray — there are corresponding positions for the reflected trans- 
versals. These directions of the incident transversals are the uniradial 
directions. 

For a uniradial direction the incident, reflected, and refracted trans- 
versals lie in one plane, and the refracted transversal is the resultant of 
the other two. 

The transversal is normal to tlie plane containing the ray and the 
wave normal. The polar plane is defined as a jDlane through the trans- 
versal and parallel to the line joining the extremity of the ray to the 
point in which the wave normal meets the surface of wave slowness, here 
designated the ' index surface.' 

It is hence proved that for a uniradial direction the incident and 
reflected transversals lie in the polar plane of the refracted ray, and then 
the principles of equivalence of vibrations and of vis viva lead to 
equations to determine the relation between the azimuths of the trans- 
versals referred to the plane of incidence. 

' lyiacCullagh, ' On the Laws of Crystalline Reflexion and Eefraction,' Januarv, 
1837, Trans, of Royal Irish Academy, vol. xviii. 



ON OPTICAL THEORIES. 159 

These give — 



tan 6 = cos (<p - f') tau 6' + si" Y tan x 

cos d' sin ((f) + f') 



(1) 



tan 0, = - cos (^ -t- d,') tan 8' + sm -»ja^nj^_ 

cos d' sin (^ — 0') 

with exactly similar formate for the other uniradial direction ; ft, 0;, and 
ti' are the azimuths of the transversals in the incident, reflected,'and re- 
fracted waves measured from the plane of incidence, and % tlie ano'Ie 
between the ray and the wave normal. In the general case the incident 
vibration is resolved into two in the uniradial directions, and each 
considered separately. When the two values of «,, found from these, are 
equal, the partial reflected transversals coincide ; the value of ^i at which 
this takes place is the deviation, and the angle of incidence the polarising 
angle. 

The theory is applied to Iceland spar, and agrees with experiments of 
Brewster and Seebeck. 

§ 4. The same problem is considered by Neumann ' in a long paper 
read in 1835 before the Berlin Academy, and in a second memoir pub- 
lished separately in Berlin 2 in 1837, and the same results deduced from 
similar hypotheses. 

§ 6. In 1839 MacCullagh ^ attempted to found his theory on a dyna- 
mical basis by finding an expression for the potential energy of the ether 
when strained by the passage of the waves of light, and applyino- to the 
expressions thus obtained Laplace's principle of virtual velocities.'^ 

This leads to a volume integral which holds throughout the space 
occupied by the medium, and a surface integral to be taken over the 
boundary. 

The surface integral taken in connection with the principle of the 
continuity of the displacement gives the conditions at the surface and 
these are shown to be identical with the conditions found in the previous 
paper. ^ 

Professor Stokes, in the Report on Double Refraction, has pointed out 
the error in the fundamental expression assumed by MacCullao-h for the 
energy, and this error of course affects the theory of reflexion. ^ 

Chapter II. — Geeen. 

§ 1. The correct expression for the energy, and the correct laws of re- 
flexion and refraction on a strict elastic solid theory, had at the date of 
MacCullagh 's paper been given by George Green * in a memoir read before 
the Cambridge Philosophical Society in December 1837. 

The potential energy of the medium is shown to be a function U) 
ot tJie three principal elongations s„ s^, s^, and the three principal 
shearing -strains a, /3, y. ft' 

,'^.^y''\"^^-'^^^Tetische Untersuchuug der Gesetze nach welchen das Licht an 
der Granze zweier vollkominenen durchsichtigen Medien reflectirt und gebrochen wird° 
dieInw'u•T;,^'^''■•.'^?^^^^^^^^' "^"^ Krystallfliichen bei der Reflexion und ttber 
^i!.r^l l"^* "^""^ gewohnlichen und ungewohnlichen Strahls.' See also ' Vorlesuo^en 
fiber tWtische Optik,' von Dr. F. Neiimann, edited by Dr. E. Dorn. Leipzi' sfs 

«r,dP t'^r"'"^.^'^'^ Essay towards a Dynamical Theory of CrystaS Reflex 'on 
and Refraction,' Tram, of Royal Irish Academy, vol. xxi. ^enexion 

Geo. Green, ' On the Laws of Reflexion and Refraction of Light at the fommnn 



160 KEPORT — 1885. 

This function is then expanded in the form 

? = V>0 + </>i + '/>2 +• • • • 

00, &c., being homogeneous functions of the orders 0, 1, 2 of the small 
quantities Sj, s^, &c. 

The equations of motion depend on '60, and so, (po being constant, it 
does not appear. If the medium in its equilibrium position is unstrained 
01 vanishes also, and in general 02 contains twenty-one arbitrary coeffi- 
cients. 03 may be neglected compared with 02- If the medium be not 
initially free from strain, 0, will introduce six more coefficients, so that 
finally we find the most general form of for our purposes involves 
twenty-seven coefficients. • 

Green then supjDOses the medium to be symmetrical with regard to 
three rectangular planes, and obtains finally as the form for f, taking the 
case in which the medium is initially strained, the value — 

_20=2A*'-f2B*^-H2C 5' 
^ civ dy az 

, ^T^ dv dvj , or\ <^" (^^y 1 OT? '^"^ ^'" 
dy dz dx dz dx dy 



+ 



+ G 



+ L 



ydz dy J \dz dx) \dy dxj ^ ^ 



If the medium be initially unstrained A=B=C=0, while, further, if 
it be completely isotropic, 

G = H = I = 2N -f-R"! 

L = M = N j» . . . . (2) 

P = Q = R. J 

And introducing two new constants, A and B, 

n^ . fdn , dv . dw\^ 

— 202 = A -- + •— + -y- 
^^ \dx dy dz ) 

. (dv dw , dw du du dv\ \ ^o\ 

\dy dz dz dx dx dy) J 

■ For the difference between this and Cauchy's theory see Prof. Stokes's report. 



ON OPTICAL THEORIES. 



161 



According to Green's theory of double refraction, founded simply on 
the supposition that the displacements are in the wave front in a crystal, 



G = H := I = /i, say 

Q=/i-2M f 



The equations of motion are given by 



j^^Mjdz[p(piu 






^-d<p\ =0 



(4) 



(5) 



In treating of the problem of reflexion this integral is applied to the 
whole of the two media, and is transformed by partial integration into a 
volume integral, which may be written 

and a surface integral, which we may write 

\dy dz (X cu — Xj cmj) 
+ dzdx(Jlv — Yylv{) 
+ dx dy {7i Iw — Zj Iw^. 

These two integrals must vanish separately. Green's work as to the 
former, on which the propagation of light depends, has been considered 
by Professor Stokes. It leads to the three equations — 

^^" /A -o\ ^ fd^*' , dv , div\ , Tj „ 9 



' df^ 



— (K — TV\ / -1- 4- ^ 4- R V7 2 
dy \dx dy dzj 



d^io 



d /du dv div^ 
dz \dx dy dz , 



p— =(A-B)^J^^ + ^ + ^^) + Bv^^« 



(6) 



which form the basis of the whole theory of isotropic elastic solids, 

§ 2. The latter integral equated to zero gives us the surface condi- 
tions ; for over the surface, according to Green, who treats the ether in 
the two media as two separate elastic solids always in contact with each 
other, we must have 

• . . (7) 

• • . (8) 



and hence 



«=Mi, t;=fi, w=-w^, 



X=Xi, Y=Ti, Z=Z,, 



These six equations determine the motion completely. 

Using Green's notation, and considering only the case of two homo- 
geneous media, let us take the plane x=0 as the separating surface. 
Then the surface conditions become 



1885. 



i(=M^, V^Vi, W = lVi, 



M 



162 



REPORT — 1885. 



\dx dy dz J \dy dz J 

. Aiwi dvj . r?WiN _ 22 A7f'i , dw^ \ 

\dx dij dz J ' V% d7. J 

rdu dv\ _ -g I'dxi _^ dvi\ 

\dy dxj ' V dy dx J 

fdu div\ _ -o (dMi ,dw^\ 
\di "^Ite; '\dz^ dx J 



B 
B 



. (9) 



when a;=0. 

The problem now resolves itself into two cases. Let ns take the plane 
of incidence as the plane xy, and suppose that the vibrations in the 
incident wave are perpendicular to this, then — 

Case I. — Light polarised in the plane of incidence, 

and the conditions are 



T-) dw -r, dw] 



dx 



dx 



} 



(10) 



Now, we have seen that Fresnel originally assumed that the rigidity of 
the ether is the same in all media, and the density different. Green, 
adopting this view, puts B=Bi, A=Ai,* and the above formula lead him 
to results agreeing with those given by Fresnel's simple theory for this 
case, while, by making the angle of i-efraction imaginary, it is shown that 
the wave, when totally reflected, undergoes just the change of phase given 
by Fresnel. 

Case II. — Light polarised at right angles to the plane of incidence, the 
vibrations being therefore in that plane. 

Then i(; = t(;i=0, and the surface conditions are 



U = U-,, V = V, 



Z«, 



" \ dx dy) dy \ dx dy ) dy 

= -R, f'^'^i^.'^ll) 



-ry/du dv 
\dy dx, 



. (11) 



J ' V dy dx 



We have here four equations to determine two unknowns, viz. the inten- 
sities of the reflected and refracted rays, and it is clear, therefore, that 
two more quantities must come under consideration. 

Now, in the general case it follows from the equations of motion given 
above that two waves can traverse the medium. In the one of these the vibra- 
tions are transverse, and travel with the velocity \/B/p. This constitutes the 
lio-ht-wave. In the other the vibrations are longitudinal, and travel with the 
velocity^ A /p. In the case before us, then, reflexion gives rise to both 
these, and we have two reflected and two refracted waves. But experi- 

* The physical meaning of these constants and the relations implied by these 
conditions will be considered later, see p. 167. 



ON OPTICAL THEORIES. 163 

ment tells us, id a bigli degree of approximation, that the whole of the 
energy of the incident light appears in the reflected and refracted light. 
"We are therefore forced to suppose not merely that the longitudinal wave 
does not affect our eyes as light, but also that it does not absorb any 
material part of the incident energy. This conclusion is confirmed when 
we recollect that on arriving at a second refracting surface this longi- 
tudinal wave would, if it existed, set up transverse vibrations which 
would be visible, so that on passing through a prism, for example, there 
would always be two emergent rays. 

Now, Green shows that very little energy will be absorbed by the 
longitudinal vibrations, provided that the ratio A/B be very small or 
very great ; and, further, that the condition of stability of the medium 
requires that A/B should be greater than 4/3. He therefore concludes 
that A/B is very great — practically infinite, or that the wave of longi- 
tudinal vibrations travels with a velocity enormously greater than that of 
light. 

The equations are then solved, assuming that B = Bj and A = Ai,* by 
the substitutions — 



eld) , d4'\ 
dz dij 

d^_d\li 

dy dx 



(12) 



The symbol represents the longitudinal or, as Sir Wm. Thomson 
has called it, the pressural wave, and \p the transverse or light wave. 

It is shown that by the reflexion a difference of phase is produced 
between the reflected and incident and the refracted and incident waves, 
and expressions are found for the intensities of the reflected and refracted 
waves in terms of that of the incident. According to these expressions, 
the mtensity of the reflected wave never vanishes, but reaches a minimum 
when f + <p'z= 90°. The minimum value of the ratio of the two intensi- 
ties will be for air and water about 1/151, while for a diamond or other 
substance of great refractive index it would be much greater still. 

§ 3. This result, then, of the theory is in direct antagonism to the fact 
that light is very nearly completely polarised by reflexion from most 
transparent surfaces at the polarising angle, while the values found for 
the change of phase do not agree with the experiments of Jamin,' 
^mcke, and others, and the theory as left by Green is certainly incorrect. 
We shall, however, return to this point later.^ 

Green does not apply his equations to the problem of crystalline 
reflexion, and, indeed, his theories of reflexion and of double refraction are 
entirely inconsistent, for the former supposes the ether to have the same 
rigidity in all bodies, while the latter attempts to explain double refrac- 
tion by making the rigidity of a crystal a function of the direction of the 
strain, 

* This last equation, as we shall see later, is not necessary. 

Jamin, Ann. de Chimie (3), t. xxix. p. 263 ; Quincke, ' Experimentelle optische 
^ntersuchungen,' Pogg. Ann. See also Haughton, Phil. Mag. (i), vol. vi. p. 81. 

* See p. 192. ^ -^ ■/' t; 



M 2 



164 EEPOKT — 1885. 

Chapter III. — Cauchy. 

§ 1. Cauchy 's optical researches were being published about this 
same period, and a very full and interesting account of them, and of the 
work of other French authors, is given by M. de St. Venant in a paper to 
which I am greatly indebted for much valuable information.' 

Cauchy 's work on elastic solids began in 1822, and in 1829 he pre- 
sented to the Academy his first memoir on isotropic media. His more 
generally known memoir followed in 1830,^ containing his work on 
double refraction and the propagation of light in a crystal. An account 
of this is given in Professor Stokes's report in 1862. His first work on 
dispersion, which he explained (following a suggestion of Coriolis) by the 
addition of terms involving differential coefficients above the second, was 
published in 1830.^ The great memoir, ' Sur la dispersion de la 
lumicre,' in which he developed this principle, appeared between 1830 and 
1836 ; ■* and in this same memoir he first considered the problem of reflexion 
and refraction, which led him to the idea of elliptic polarisation and 
a more general expression for the possible displacements of a molecule * 
in a plane wave. 

§ 2. Further considerations on the subject of reflexion and refraction 
led him to conclude that, in order to obtain Fresnel's expressions for the 
intensities of the reflected and refracted rays in terms of that of the 
incident, it was necessary that not only the displacements, but their 
differential coefficients with respect to the normal to the surface of 
separation, should be continuous across that surface. This continuity 
had to be rendered compatible with the rest of his theory, in which the 
ether is considered as differing both in density and elasticity in different 
media.'* It is, however, quite inconsistent with the true surface con- 
ditions established by Green, Neumann, and MacCullagh on their various 
hypotheses — the conditions, namely, that the displacements and the stresses 
over the surface should be the same in the two media; and Cauchy, in con- 
sequence, was led to conclude that the method of Lagrange, by which the 
above conditions were first established, is inapplicable to questions of this 
kind.^ But, as St. Venant points out, these sui-face conditions do not in 
the least depend on Lagrange's method of virtual velocities, but on the 
fundamental elementary principles of mechanics, and can never be recon- 
ciled with Caucliy's theory of continuity so long as it is supposed that 
the rigidity of the ether varies from one body to another. 

§ 3. In 1839 * Cauchy re-established his equations of motion for an 
isotropic medium, basing them on analytical considerations of symmetry. 
For a perfectly isotropic body he arrived at the equations — 

p^=(A-B)f + Bv2« . . . (13> 
dt'^ dx 

, „ dti , dv dw 

Ac, where ^ = Tx'^^j^^' 

' De St. Venant, 'Sur les diverses mani^res de presenter la thSorie des ondes- 
lumineuses,' Ann. de Chimie (S. iv.), t. xxv. p. 335. 

" Cauchy, Exercices de Mathcmatiqncs, t. v. pp. 19-72. 
' Cauchy, Bidletin de M. dc Fcrusmc, t. xv. p. 9. 

* Noum-aux Exercices de Mathimatiques. * C. It. t. 'vii. p. 867. 
» a R. t. viii. p. 37i ; t. x. p. 266. 
' C. R. t. xxvii. p. 100 ; t. xvi. p. 1.54 ; t. xxviii. pp. 27, 60. 

• C. R. t. viii. p. 985; Exercices d'Anahjsc, t. i. p. 101. 



ON OPTICAL THEORIES. 165 

already given by Green. ^ And in cases in whicli the axes can only be 
turned together aboat the origin, a third coefl&cient comes in, in the form 
of terms, such as 

p fdw dv 



\dy 



_dv\ 
dzj' 



In 1849 ^ Cauchy propounded the idea that the ether atoms in a body 
such as a crystal are disposed, as it were, in shells round the matter atoms 
in such a manner as to have different elastic properties at different points 
of the same shell ; the shells, however, are regulai'ly placed, and the 
properties of the ether repeat themselves at similar points in the different 
shells. It results from this that the constants in the equations of motion 
will be periodic functions of the equilibrium positions of the molecules, 
and for optical effects we hare to do with the average displacement over 
a small volume of the medium.^ 

The general equations established by Cauchy lead to a normal wave 
travelling with a velocity equal to \/A/p. According to his earlier theory, 
resting on the law of action between the molecules of ether, A and B are 
not independent, and it is possible by suitably choosing the law of force 
to make A vanish or even be negative. The theory * of reflexion and 
refraction led him to conclude that A was a small negative quantity, so 
that the normal disturbance ceases to be propagated as such. 

§ 4. Canchy's work was continued by Briot,' starting from the 
equations of motion deduced from the mutual action between two par- 
ticles of ether, and the supposition suggested by Cauchy that the ether 
within a crystal is in a state of unequal strain. In treating of dispersion 
Briot points out that it cannot be explained in the manner originally 
suggested by Cauchy, for there is no reason why the terms in his differ- 
ential equations from which it arises should be insensible in a vacuum if they 
are sensible in ordinary transparent media. He therefore makes it depend 
on terms arising from a periodic distribution of the ether within material 
bodies, and shows that to obtain Cauchy's dispersion formula the law of 
action between the molecules must be as the inverse sixth power of the 
distance. In his memoir on reflexion and refraction, however, he adopts 
Cauchy's views as to the disappearance of the normal wave, and this is 
quite inconsistent with the above law, while the ether and matter mole- 
cules must attract each other with a force varying as the inverse square 
of the distance. 

§ 5. The problem of reflexion and refraction for both isotropic and 
crystalline bodies is treated of in a memoir published in 1866-67,^ start- 
ing from Cauchy's principle of continuity, to which he gives an extended 
meaning in the second memoir. He at first supposes the vibrations in 
the crystal to be rigorously in the plane of the wave, and, adopting 
MacCuUagh's methods of the uniradial direction, arrives at his equations. 
The work is then extended to the general case in which the vibrations 



o^ 



' See p. 161. 

' a R. t. xxix. pp. 611, 644, 728, 762 ; t. xxx. p. 27. 

' For the further development of this by M. SaiTau, see p. 174. 

* C. R. t. ix. pp. 677, 727, 76.5. On this point cf. Green's theory. See also 
Stokes's, Brit. Assoc. Report, 1862, and pp. 170-195. 

* Briot, Essais siir la theorie mathematiqiie de la lumiere. Paris, 1861. 
' Liouville's Jouriial, t. xi. p. 305 ; t. xii. p. 185. 



166 EEPOBT— 1885. 

are quasi-transversa], and it is shown how the simpler forms of the 
equations are modified by this. 

Thus, for the uniradial directions in the case in which the longitudinal 
disturbance is supposed to be strictly normal to the wave, if ^ is the 
angle between the ray and the wave normal, 6, 6', and 0, the azimuths 
of the planes of polarisation, measured from the plane of incidence, of the 
incident reflected and refracted waves, (p and f' the angles of incidence 
and refraction, and m a quantity depending on the angle between the 
plane of the wave and the direction of vibration, then — 



tan 6 = tan 0' cos (0 — (//) + -. — -~ —^ 

cos sin (</< -t- ?' ) 

, /■; /. . /\ '"' sin^ (/>' tan v 

tan 0, = tan 0' cos (^ + 0') — ^ ^ 



(14) 



cos W' sin ((^ — 9') 
These formulte agree with those of MacCullagh if we put m = 1. 

Chapter IV. — Elliptic Polarisation. Compaeison of Results, 

§ 1. The peculiar phenomena presented by quartz had been explained 
by Airy in 1831 ^ on the assumption that the two waves were elliptically 
polarised. In 183G ^ MacCullagh made a further advance, and showed 
how the addition of certain terms to the diflFerential equations of motion 
would lead to the elliptic polarisation required by Airy's theory. The 
equations assumed by MacCullagh, for the existence of which he does 
not attempt to assign a mechanical reason, were — 



Ti^ ~ 7f-? Iff , 
Where A ^ a\ B = a" - {a" - 1"") sin^ 9, 



(15) 



a and h being constants, and the angle between the optic axis and 
the wave normal — the axis of z. The two waves resulting from these 
equations are shown to be elliptically polarised, while their velocity is 
given by the equation 

K-A)(i.^-B) = ^ . . . (16) 

X being the wave length. The rotation of the plane of polarisation 
produced by the passage of a plane polarised ray through a plate of 
crystal cut at right angles to the axis, and of unit thickness, is 'l-Jz'^Cja^X^. 
MacCullagh shows that the results of this hypothesis as to the form 
of the equations agree fairly with Airy's experiments, and that the 
agreement would be made somewhat more close by the hypothesis that C 
varies slightly with 0. 

' Airy, ' On the Nature of tlie Two Eays produced by the Double Eefraction of 
Quartz,' Camh. Phil. Soc. Trans, vol. iv. pp. 70, 198. 

^ MacCullagh, ' On the Laws of the Double Refraction of Quartz,' Irish Trans, 
vol. xvii. p. -IGl. 



ON OPTICAL THEOEIES. 167 

§ 2. Terms of a similar kind were first applied by Airy ' to explain 
the magnetic rotation of the plane of polarisation discovered by Faraday. 
Airy starts by calling attention to the fundamental difference between 
the rotation produced by quartz and that due to magnetic action. In 
quartz, sugar, etc., by reflecting the ray back along its original path the 
rotation is reversed, so that the ray emerges with its plane of polarisation 
unaltered, while in bodies under magnetic action the rotation is doubled 
by the same process. It is as if the former effect were due to a heliacal 
arrangement of the molecules, the latter to a continuous rotation of them 
round the lines of force. Airy shows that the effects produced can be 
accounted for by the introduction into the equation for u of terms 
involving odd differential coefficients of v with respect to the time, and 
he works out the case in which the equations are 



W ~~ dz^ dt 

cPv . d^v _ f>,dzi 

clr'~ d? dt . 

The two possible velocities for a wave of period r are given by 

Vi^ =■ — ■ , f -J = . 



(17) 



It is pointed out also that terms such as — r — or would also 

dz^dt dfi 

lead to the effect observed ; though they would differ in the law, express- 
ing the relation between the velocity and the wave length. Airy 
remarks that ' the equations are given, not as offering a mechanical 
explanation of the phenomena, but as showing that they may be ex- 
plained by equations, which equations appear such as might be intro- 
duced by some plausible mechanical assumption.' 

§ 3. The attempt to estimate the relative value of the theories of 
reflexion and refraction just developed is rendered easier if we consider 
the physical meaning of the two constants involved. The importance of 
this has been continually insisted upon by Sir Wm. Thomson ^ in his 
numerous writings on the subject of elasticity, which have done so much 
to clear away difficulties and obscurities ; and though these writings 
belong to the later period of our subject, we shall consider here some of 
the results they lead to. 

To Green, Cauchy, and MacCullagh, A and B are constants, appearing 
m the most general form of the equations, and on which the rate of propa- 
gation of waves depends ; their connection with the other physical pro- 
perties of the solids is not considered. Now an isotropic 'elastic solid is 
one which possesses the power of opposing resistance (1) to change of 
shape, (2) to change of volume, and has in consequence only two prin- 
cipal moduluses of elasticity. 

' -^iiTi 'On the Equations applying to Light under the Action of Magnetism,' 
PMl. Mag. (.S), vol. xxviii. p. 469. 

" See especially, Thomson, ' Elements of a Mathematical Theory of Elasticity,' 
Phil. Tram. 1856, p. 481 ; Thomson and Tait, A Treatise on Natural Philosophy, 
vol. i. ; Thomson, article ' Elasticity,' Encyclojitedia Britannica, ninth edition, 1880. 



168 KBPOET — 1885. 

On fhe value of the one, the rigidity, n, in the notation of Thomson 
and Tait, depends the resistance which the body can oppose to a stress 
tending to produce distortion or change of shape without change of 
volume, and it is measured by the ratio of the shearing stress — or stress 
tending to produce distortion — to the strain or alteration of shape pro- 
duced. It can be shown that this is equal to the constant, B, of Green's 
theory. And the velocity of a wave of transverse displacement, since it 
does not produce changes in the volume of the body through which it 
passes, depends only on the ratio of the rigidity to the density. 

On the value of the other principal modulus depends the resistance 
which the body can ofier to compression or change of volume when sub- 
jected to a uniform hydrostatic pressure at all points of its surface. The 
compression produced is measured by the ratio of the change in volume 
to the original volume, and the modulus of compression, k, is the ratio of 
the stress to the compression it produces. 

It has been shown by Thomson that the relation between A and the 
principal moduluses is given by the equation A =: 7^ + f n, so that 1c, the 
modulus of compression, is equal to A — fB. 

The expression for the stresses arising from simple elongations e,f, g 
in the directions of the axes, and from simple shears a, /3, y round the 
axes, are found ; they are 

^, = (h + in)e+ (lc-in)(f+g) 

= {k + |n)(e +/+ g)-2n(f + g) 

. fdu ,dv dw\ _ Q-D fdv clio\ 

\dx dy dzj \dy dzj^ 

etc., using Green's notation, and 



= na =Bf 



dz dy) ' 

etc., and from these Green's expression for the energy can be obtained. 
We may note that the velocity of propagation of the longitudinal waves 
^/ A/p depends on both the modulus of compression and the rigidity. 

According to the mathematical theories of Navier, Poisson, Cauchy, 
and De St. Venant, there is a definite relation between n and h for all 
bodies given by the equation n =■ ^h or B ^ ^A. Stokes ' was the first 
to point out that this could not be true universally, and this conclusion 
has been confirmed by the experiments of Wertheim and Kirchhoff for 
various metals. 

Thus, on the assumption that the properties of the ether are those of 
an elastic solid, Cauchy's theory in its original form, independently of the 
consideration of his surface conditions, must be rejected. In his later 
theory, as we have said, he does admit the second constant A.^ But, we 
have seen that the existence of the two constants A and B implies that 
there will be two waves in the medium, while the absence of the wave of 
normal vibrations in light, combined with the conditions of stability, 
requires that A should be great compared with B, and this again requires 
that h, the modulus of compression, should be great compared with n, the 

* Stokes, ' On the Friction of Fluids in Motion and the Equilibrium and Motion 
of Elastic Solids,' Trans. Camh. Phil. Soc. 1845 ; Math. Papers, i. p. 75. 
2 See pp. 164, etc. 



ON OPTICAL THEOEIES. 169 

rigidity. Thus we are compelled to treat the ether as an elastic solid of 
very great — practically infinite — incompressibility. Now, the cubical 
dilatation produced by a given state of strain is measured by e +/+ g, or 

— + — + — , and the condition of incompressibility requires that this 
dx dy dz 

should be zero. It is not, however, admissible to omit the terms in 

e+f+g in the equations, for they occur with the constant A as a factor, 

and the physical condition that these terms should vanish implies also 

that A should be very large. To obtain the correct equations we must 

put 

/ K -DN ^du , dv , dw\ 

^^-^UJ.+ di,^'d^)==-^' 
and they then become 

4>-| + Bv%. . . . (18) 

et cetera. 

§ 4. MacCuUagh and Neumann omit the terras in p entirely from 
their equations, both within the medium and over the surface, and are led 
in consequence to erroneous results, though, as we shall see later, their 
theories (modified so as to include the terms) have been developed by 
Lord Rayleigh ' and Lorenz. Green, as we have seen, is perfectly con- 
sistent throughout ; but his final equations, unfortunately, are not con- 
firmed by experiment. If we assume the rigidity of the ether to be the 
same in the two media, it is not difficult to show that Cauchy's surface 
conditions are identical with those of Green, or, to be more accurate, that 
Green's correct equations expressing the continuity of the stress and of 
the displacement over the surface reduce to Cauchy's. Green obtains his 
surface condition from the value of a certain integral over the surface ; 
they may be obtained, perhaps more simply, from the equations of motion 
of an element dS of the surface ; for, taking the case when the plane x=0 is 
the bounding surface, let v be the thickness of the element, Nj, N/ the 
stresses on it parallel to the axis of x, then we have 

prdS'^^=(Ny-TS,')dS . . . (19) 

Hence, when v is indefinitely decreased, N,=Ni', with other similar 
equations. On Green's supposition that A^A,, B^Bj, these conditions 
for Case I. (vibrations normal to the plane of incidence) lead to 

div _dwi , " • • • . • • (^^) 
dx dx 

and for Case II. (vibrations in the plane of incidence) to 

du dui dv dvi 't • • (^U 

dx dx ^ dx dx' } 

which are Cauchy's conditions. The difi'erence between the two theories 
lies in their treatment of the waves of longitudinal displacement. 

> See p. 189. 



170 REPORT— 1885. 

According to both Green and Cauchy they depend on a function 0, 
where 

,p = ,p^e ""'■'' + "'■'■''"> .... (22) 
And in both theories 

a'2 + &2 = ^ (23) 

Green puts A/p very large, so that a'^ + h'^=0, and 

(j) = ei'-'^IK sin (hj + ct) + Lcos (hij + ct)} . . (24) 

while Cauchy, without any dynamical justification, writes A/^=— c^/P, 
k being a large quantity, so that A is a small negative quantity. Hence 
a'^ + b^= -P. 

The assumption of a negative value for A leads to the conclusion that 
the modulus of compression is negative — that is, that the medium is such 
that pressure causes it to expand and tension to contract, and this alone 
is fatal to the theory. 

§ 5. We come, then, to the conclusion that the phenomena of reflexion 
and refraction cannot be explained, any more than the phenomena of 
double refraction, on a purely elastic solid theory involving a sudden 
change of properties on crossing the interface. Green's theory is the 
only possible consistent one, and it, in its original form, leads to results 
differing from experiment. 

Part II, — Modern Developments of the Elastic Solid Theory. 

We now come to the consideration of rather more modern investiga- 
tion on this subject. The limits of space will confine us to the theoretical 
work which has been done. The great experimental researches of Fizeau, 
Jamin, Quincke, Cornu, and others, will only be occasionally referred to. 
A complete account of these must be left for some future time. 

Chapter I. — General Properties op the Ether on the Elastic 

Solid Theory. 

The elastic solid theory of the propagation of light and double refrac- 
tion has been discussed in various papers by Haughton, Lame, St. Venant, 
Boussinesq, Von Lang, Sarran, Lorenz, Rankine, Loi'd Rayleigh, Kirch- 
hoff, and others. 

§ 1 . Haughton considered the problem of the general equations of an 
elastic solid in a paper read before the Irish Academy in 1846, in which 
he adopts Cauchy's views as to the constitution of the medium. These 
views are modified in a second paper,' read in 1849, in which the general 
equations are formed, and the correct expression found for the potential 
energy. 

In this paper Haughton shows how to calculate the strain in any 
direction produced by a given elongation in the same direction. This 
strain is proved to be inversely proportional to the fourth power of the 
radius of a certain surface, called by Rankine the tasimonic surface. A 
form is found for the equation to the surface of wave slowness, which is 
said to reduce to MacCuUagh's if the vibi'ations be strictly transversal ; 
but, in making the reduction, the dilatation is equated to zero, its co- 

' Haughton, ' On a Classification of Elastic Media and the Law of the Propaga- 
tion of Plane Waves through them,' Irish Trans, vol. xxii. p. 97. 



ON OPTICAL THEORIES. 171 

efficient remaining a finite quantity, and in conseqnence the results are 
erroneous. 

§ 2. Lame is the author of numerous papers, in the ' Comptes 
Rendus ' and elsewhere, on the propagation of waves througli an elastic 
medium, and his results are summed up in his ' Le9ons sur I'Elasticite.' '' 
The general form of the equations for the strains are shown to contain 
twelve constants, which become six if the dilatations be equated to zero, 
and three when planes of symmetry are taken for the co-ordinate planes. 
The equations of motion finally obtained may be written 

W~'^'di! \dy~~dx) ~" 'Lh\Iir~ d^J ' • '< ^' 

etc., which agree with MacCullagh's and with Green's if we omit the 
terras involving the dilatation. The arguments to be advanced against 
the theory are identical, then, with those which Professor Stokes has urged 
against MacCullagh's. 

§ 3, St. Venant has written many most important papers on the 
subject of elasticity. He still adheres to Cauchy's theory and the form of 
the equations of an elastic solid deduced from the hypothesis of direct 
action between the molecules of the medium, and in his last great work 
on the subject, the annotated French edition of Clebsch's ' Elasticity,' 
states his reasons for so doing in §§ 11, 16. However, in the work he 
employs Green's expression for the energy, with the twenty-one co- 
efficients — ' Vu la controverse actuelle ou la majorite des avis est con- 
traire au notre.' 

§ 4. In It paper printed in 1863 "^ he criticises Green's theory of double 
refraction, arguing that Green's conditions for the tranversality of the 
vibrations lead to isotropy. This conclusion is frequently repeated in St. 
Venant's ^ papers, and it will therefore be well to investigate the point 
somewhat closely. 

Let us suppose that we have a simple elongation e in a direction 
li, mj. 111, i^ ^ medium falfilling Green's conditions. Let I.2, mo, n^, I3, 
TO3, ^3 be the direction cosines of two lines at right angles in a plane 
normal to Z,, TOj, n^, and let us investigate the stresses N/, Ng', N3', 
T/, T2', T3' on the faces of an element normal to these directions. Then 
St. Venant's argument rests on the fact that N/ is independent of the 
direction of the elongation, while Ta'and T3' vanish, and that this would 
be the case in an isotropic medium. This last statement is of course 
true, but on Green's theory Na'. ^3' ^o depend on the direction, which 
they would not do in an isotropic medium, and T/ has a finite value, 
while for an isotropic medium it would vanish. 

The values for the stresses may be shown to be — - 

1^2'= (iU-2(LZ32-|-MTO32 + ]^n32)}J 

N3'={yu-2(LZ2^-j-Mm22-i-N„,22)}.l , . (2) 
T/ = 2 {hlj3 + Mi».,m3 + Nnjng) e 
T2' = T3' = 

J Lame, Zegonit sur I'Elasticite. Paris : Gauthier Villars, 1866. 
■^ St. Venant, 'Sur la distribution des elasticitSs autour de chaque point d'lm 
solide,' LiouviWs Journal, S. ii. t. viii. p. 257. 

3 See especially De St. Venaiit, 'Theorie des ondes lumineuses,' Aim. de Cldm. 
S. IV. p. 22. 



172 REPORT — 1885. 

For an isotropic solid we should have Nj' = N3' =: (yu — 2L) e and 
T/ = 0. Thus Green's medium in which the propagation of transverse 
waves is possible has properties which distinguish it fi'om an isotropic 
solid, for a simple elongation produces on any plane parallel to the direc- 
tion of the elongation a normal stress which depends on the position of the 
plane, while it also produces shearing stress about an axis parallel to the 
direction of the elongation ; and although the theory does not explain 
double refraction satisfactorily, yet it is not open to De St. Venant's criti- 
cisms on this point. 

§ 5 In the same jDaper St. Venant proposes a modification of Cauchy's 
theory which leads to Fresnel's wave surface without any more conditions 
than are required by Green ; for, putting in Green's expression, 

AZ2 + Bm2 + 0^2 = X . . . . (3) 

I, VI, n being the direction cosines of the wave normal, the equation to 
■determine the velocity becomes — 

{p V2 - X - G/2 - Hm2 - Iw2} [(p V2 - X)2 - (p V* -X) 

{(M + N)Z2 + (N + L)m2 + (L + M) n^} + MNZ^ + NLjn^ -j- LM«2] 

- {(H - L) (I - L) - (L + P)2} {GZ2 + Nto2 + M».2 + X - pV^} mhi" 

- {(I -M) (G - M) - (M-t- Q)2} (NZ2 + Hm2 + Ln^ + X - pY''}nH'^ 

- {(G - N) (H - N) - (N + R^2} {MP + hw? + In"^ + X - pV^} Vm'' 
+ {(G - M) (H - N) (I - L) + (G - N) (H - L) (I - M) 
-2(L-|-P)(M + Q)(N + R)}Z2»i%2 = (4) 

And this will reduce to Fresnel's surface if A = B = C ; that is, if the 
equilibrium stresses are equal, and the four conditions 

(H-L)(I-L) = (L + P)2 X 

(I-M)(G-M) = (M + Q)2 

(G - N) (H - N) = (N -h R)2 !" • (5) 

(G - M) (H _ N) (I - L) + (G - N) (H - L) (I - M) 

-2(L + P)(M-l-Q)(N + R)=0 
are satisfied. 

These equations include those of Green's first theory, and are approxi- 
mately those which arise from what St. Venant calls an ellipsoidal 
distribution of elasticities. Under certain circumstances the tasinomic 
surface — which, it will be remembered, gives the tension in any direction 
produced by a simple elongation in that direction — reduces to an ellipsoid, 
and then the distribution of elastic constants is named by St. Venant 
ellipsoidal. This distribution is produced when an isotropic medium is 
unequally sti'ained in three perpendicular directions. The theory is 
interesting, and important as showing that Fresnel's wave surface can 
be deduced from the general elastic solid theory on other assumptions as 
regards the constants than those given by Green, and that the vibrations 
in this case are not necessarily in the wave front. There will, however, 
in this case be a quasi-normal wave, the velocity of which is given by the 
equation 

p72 _ X- GZ2 - Hm2 - I/i2 = ; 



ON OPTICAL THEOBIES. 



173 



and if Green's arguments as to the relative magnitude of the constants be 
still supposed to hold, the quasi-normal wave will disappear, and the 
vibrations will be very neai'ly indeed transversal. The theory, however, 
interesting as it is, does not enable us to overcome the difficulty of 
reconciling the theories of double refraction and reflexion so long as we 
adopt the view of Fresnel and Green, that the latter depends on difference 
of density, not of rigidity, in the two media. It is also open to the 
objection that if the medium be incompressible the displacements must 
be in the wave front, and we must get in this case Green's conditions, 
not the above ; while if the medium be not incompressible an appreciable 
amount of energy must exist in the form of longitudinal vibrations. 

§ 6. The question of the propagation of waves through an isotropic 
medium, which is rendered anisotropic by the production of three elonga- 
tions, a, h, c, in three rectangular directions, has been studied by 
Bonssinesq.^ The elastic constants are taken to be linear functions of 
these permanent strains, and the number of constants involved in their 
expression is reduced from the considerations involved in the symmetry 
of the medium and the principle of the conservation of energy. 

The equations of motion may be written 






= (X + Va)'j? + (/z + pa)v 



dx 



■u 



+ «T 



{d'^u , T d^u , 



dy' 



dH \ 



dx 1 dx dy dz . 



(6). 



with the condition implied by the principle of the conservation of energy 
that \'= I', while if the normal stresses in the equilibrium condition 
vanish a = p. These may be deduced fi-om Green's equations by putting 



A=((7-p)a, B = ((T-p)&, C = ((r 



py, 



(7) 



with similar expressions for the other constants, A and fi are the two 
elastic constants of the nnstrained medium in the form in which they 
are written by Lame, v/X and ^/(X + fx) being the velocities of trans- 
verse and normal waves respectively, the density being taken as unity. 
_ _ It is thus shown that on the assumption that a, b, c are small quan- 
tities, such that their squares and products may be neglected, Fresnel's 
wave surface is given if either u =0 or o- = p. In fact, the condition «r = 
leads to Fresnel's surface without any assumption as to the value of 
a, h, c, for then the theory becomes identical with Green's second theory ; 
while if (T=zp we have either St. Tenant's ellipsoidal condition or his 
suggested modification of Cauchy, for to this degree of approximation the 
two theories are identical. 



Boussinesq, Liouville's Journal, S. ii. t. viii. 



174 



REPORT 1885. 



"We may conclude, then, that Fresnel's laws as to double refraction 
would hold in a medium strained in the manner Boussinesq considers, 
but the theory as a whole is liable to the same criticisms as have been 
made to Green's. Boussinesq is the author of another and different 
theory, which we shall consider later, and which gives a better explana- 
tion of the phenomena. 

§ 7. This same problem has been dealt with by Professor C. Niven,' who 
has arrived at similar results without introducing considerations based 
■on molecular reactions. 

§ 8. The problem of double refraction has been treated in a different 
manner by M. Sarrau, following up the suggestions of Cauchy as to the 
nature of the ether in a crystal, aud his theory is developed in two papers 
in ' Liouville's Journal.' In these papers^ the density of the ether in a 
transparent medium is supposed to vary in a periodic manner from point 
to point. The ether is arranged in concentric shells of variable den- 
sity round each matter molecule, and its density, variable round each 
matter molecule, is the same at any one of a series of points situated 
similarly with regard to the matter molecules. The ether is periodically 
homogeneous, and the coefficients which occur in the elasticity equations 
are no longer constant, but are pei-iodic functions of the co-ordinates of 
the point whose displacement is being considered ; from these equations 
^are deduced a series of others with constant coefficients, containing the 
;average displacements of the ether in an element of volume. It is to 
•these average displacements that optical effects are supposed to be due. 

Cauchy ^ has indicated the path to be followed in deducing these 
auxiliary equations from the fundamental forms, and M. Sarrau arrives 
.at the following conclusion. 

If the fundamental equations be represented by 



df" \dx' dy' ihJ ' ' V 

^=«(- • • ■) 

?=H(. . . .). 



dt 



(8) 



"Where F, G, H are functions v?ith periodic coefficients of u, v, w and 
their differential coefficients, then the auxiliary equations will be — 



d^u 



= F' + G' + H' 



(Py_ ^ Y" + G" + H" h 
dt^ 

d^w ffi/// I n.'// I TT/'/ 



(9) 



' C. Nlven, Quarterly Journal of Pure and Ajyplied Mathematics, No. .55, 1876. 
* Sarrau, C. R. vol. Ix. p. 1174. ' Sur la propagation et la polarisation de lalumifere 
•dans les cristaux,' Liouville's Journal, S. ii. t. xii. p. 1 ; t. xiii. p. 59. 
' Cauchy, Comytes Jtendus, t. xxx. p. 17. 



ON OPTICAL THEORIES. 175 

F', F", F'" being symbolic functions obtained by substituting integral 

functions of — , — -^ for the periodic coefficients of F, and similarly for 
dx chf dz 'J 

G', H'. 

The second memoir ' is devoted to the consideration o£ the problem on 

the supposition that the ether in a crystal is isotropic as regards its 

elasticity, and that the variations in density are all which we have to 

consider. Again following Cauchy, and treating the ether as a system of 

attracting and repelling points, Sarrau arrives at the equations 

<|-r=E(v> + r(v')|}. . . . (10) 

etc., where E and F are certain connected functions depending on the law 
of force, and d the dilatation. 
For free space — 

E(v2)=ev2, 

F(v2)=/, 
e and / being constants. 

For the ether in a crystal, omitting the consideration of dispersion, it 
is shown that it is probable that E and F have the same forms, only 
now e and / are periodic functions of the co-ordinates. 

If we denote djdx, djdij, d/dz, djdt by a, /j, y, a, respectively, then 
the equations in the crystal become, in conformity with the general rule, 

«r%= V2(F,« + F,v + F3M;) + (/,« +/;/3 +/37)9, 

etc., where F, G, H, etc., /, g, h, etc., denote now symbolic functions of 
«, /3, y. 

These general equations are simplified by the consideration of the 
various kinds of symmetry possible, and it is shown that in the case of 
ordinary biaxial crystals they reduce to 

dho ,.„2 , .• M^ 



^'«_.„2 . (M 



_=^v^. + ^,-^, • • • • (11) 

d'^w , , ^ dd 

It is further assumed that f + fi ^= g + gi = h + h := 0. This, of 
course, is the condition that the velocity of the normal wave should be 
zero. 

These equations are solved by putting M=:Pe*('^+'"2'+»^-<"0, etc., and 
lead to ■ 

_P__ Q _ R ^ -(Fl+Qm + Rn), 



whence 



fl gm Tin 

y^—f <^^ — g 0)2 — A 

■' ■ "' +7^=0- • • . (12) 



(li^—f w^ — g w^ — h 
' Ziouville's Journa.!, Ser. ii. t. xiii. p. 69, 



176 KEPOKT — 1885. 

Thus the wave surface is Fresnel's. The direction of vibration, the ray 
and the wave normal are shown to be in the same plane, but the direction 
of vibration is at right angles to the ray instead of to the wave normal. 

The assumed conditions / + j\ = 0, etc., form a serious objection to the 
theory as it stands, but on this point it is capable of modification. The 
vibrations, of course, are not strictly transversal within the crystal, but 
I am not aware of any experiments which prove that they must be so. 
Of course, if the medium be absolutely incompressible, the displacements 
must be in the wave front, and the theory fails ; but the condition of 
stability and the evanescence of the longitudinal wave require merely that 
the incompressibility should be very great compared with the rigidity, 
without being absolutely infinite. 

§ 9. M. Sarrau has considered the peculiar phenomena presented by 
quartz, and shows how on his theory the terms assumed by MacCullagh 
will arise. 

For the crystalline symmetry of such a body, the equations are shown 
to take the form — 



dt^ •' \ dxj •" Kdij dzj 

d^v /„, dd\ . „2 /' <^^' , <^w^ 

d^w /„o dd\ , „2 /' t^^ I <i'"\ 



i 



(13) 



and it follows that two elliptically polarised waves can traverse the 
medium in any given direction. 

The velocities of these waves are given by 

-'=f7-|(:/-/)sinM ±l^{(sr_/)2sin4 

+ }^ (g.cos'^d + f.sm^O) x(g,cos^e-g,sm^d)^ . (14) 

fy and gf, are two constants which are probably very small, and, in that case, 
the squares of the principal velocities at right angles to the axis are/ 
and g, while the squares of the velocities parallel to the axis are given by 

If pi represent the ratio of the axes of the ellipse in the ordinary wave, 
P2 that in the extraordinary, then 

q^ cos^ fl — 9 1 sin^ ,-, r\ 

^"'^-■^2Cos=^a + /,sin^0 • • • ^^^^ 

The major axis of the extraordinary ellipse is perpendicular to the prin- 
cipal plane, that of the ordinary ellipse is in the principal plane, while the 
two waves are polarised in opposite senses. 

§ 10. De St. Venant ' criticises the theory in the following points, p being 
the only periodic variable, the equations, he argues, should be treated as if the 

' St. Venant, ' Sur les diverses mani^res de presenter la theorie des ondes Inmi- 
neuses,' Ann. de Chim. (4), t. xxv. p. 335. 



ON OPTICAL THEOKIES. 177 

periodic coefficient Tvas attached to the first term, p — —^ etc., and he states 

that the development of the equations p = . . . . leads to different 

results. Sarrau,' in reply, points out that this depends on the relative 
magnitudes of the quantities a, ft, y, a^, and the other parameters ; on 
making the same suppositions in the two cases the results, he shows, are 
identical. One may, however, start from the general equations of an elastic 
solid with two coefHcients, and, by supposing the coefficients to be periodic, 
arrive at the general equations already found. 

M. de St. Venant finds a difficulty in explaining dispersion, for in an 
isotropic medium the periodicity of the coefficients vanishes. This may 
be true, and yet the equations contain differential coefficients above the 
second. 

§ 11. The theory advanced by Von Lang ^ might perhaps more strictly 
be considered under the next section : ' Theories based on the mutual 
action between matter and the ether.' The theory is, however, so slio-ht 
a modification of the ordinary elastic solid theory that it will be more 
convenient to deal with it now. 

Von Lang supposes that the displacements which come into the 
ordinary elastic solid theoiy are displacements of the ether relative 
to the molecules of the matter. He assumes that the ratio of the 
matter displacement to that of the ether is in general a function of the 
direction, but that for three directions we may write 

U=a2^t, V=i2y, W=c2m;, 

U, V, "W being displacements of matter, «, v, w of ether. 

He then forms the equations of motion, and, equating the velocity of 
the quasi-longitudinal wave to zero, arrives at Fresnel's wave surface. 
The theory cannot be regarded as having any real physical signification, 
for the elastic forces produced in the ether will depend on the real dis- 
placements of the ether particles, not on the displacements relatively to 
the matter, and the velocity of the normal wave cannot vanish, for if it 
does the medium becomes unstable. 

§ 12. Von Lang ^ has also given a theory of circular polarisation, 
which consists in adding to the ordinary equations terms such as 

.-2 fdv _ dw\ 
\dz dyj' 

From this it follows that the velocity in a medium such as sugar is 
g^ven by 

'Ztv a 
L being the wave length in air ; while in quartz 

0,2 = a2 _ «l-_^8in20 ± 1 / I (^2 _ ,2)2 8in49 

-j-^-^cos^flj . (16) 

Sarrau, ' Observations relatives k I'analyse faite par M. de St. Veuant,' Ann de 
Chim. (4), t. xxvii. p. 266. 

^ Von Lang, ' Zur Theorie der Doppel-Brechnng,' Wied. Ann. t. clix. p. 168. 
' Von Lang, ' Zur Theorie der Circular- Polarisation,' Pogg. A?m. t. cxix. p. 74. 
1885. -^ 



178 REPORT— 1885. 

Von Lang holds that the experimental law connecting the rotation 
and the wave length is 

h' 
Rotation ^h + -\- . . . . 

and this is given by the above expressions if 

a2 = m + -+ . . . . 



P = rh + ;' -f 



s 
L 



No reason is given for assuming the form 2^^^ •— — — - j rather than 

A 

that selected by MacCuUagh, o^f --^ — ^ ), which leads to the correct 

relation between the rotation and the wave length without any violent 
supposition as to the form of o^, such as is made by Von Lang ; and, 
though neither theory has any mechanical basis, this fact alone is suffi- 
cient to render MacCullagb's the more probable, while experiments on 
the size of the rings produced when convergent polarised light is trans- 
mitted through a plate of quartz cut at right angles to the axis agree 
rather better with MacCuUagh's form than with Von Lang's. 

§ 13. Another theory of double refraction was developed by Lord 
Rayleigh ' in 1871. It had been suggested originally by Rankine,^ and 
Stokes in his British Association Report referred to it, and showed that in 
its original form it was untenable. The theory is also given by Boussinesq 
in a paper in ' Liouville's Journal,' ^ which will be considered in full under 
the next section. 

Lord Rayleigh points out the inconsistency already referred to be- 
tween the theories of double refraction and reflexion given by both Green 
and Cauchy, while, as we shall see when considering the polarisation 
phenomena accompanying the reflexion, difl"raction, and scattering of 
light, he believes that Neumann and MacCullagh, though consistent, 
were wrong throughout. He then remarks that the analogy of a solid 
moving in a fluid would suggest that the first effect of the matter mole- 
cules in a transparent body would be to alter the apparent density of the 
solid, and that conceivably this alteration might depend on the direction 
of vibration. He supposes that the statical properties of the ether are 
not altered by the presence of the matter, and the equations of motion 
may be written 

d'^U dp , -n^o 



I 



d^v dp , -D„o 
P — s = - + B V"^« 

^vdf- dy 

d-lV dp , -r,„-y 

^T/2 = 7 + ^^ "^ 

where p is written for A?, c being the dilatation. 

' Hon. J. W. Strutt, ' On Double Kefraction,' Pkil. Mag. June 1871. 
^ Kankine, Phil. 3Iag. June, 1851. ' See p. 215. 



(17) 



ON OPTICAL THEORIES. 179 

Lord Rayleigh further assumes the medium to be absohitely incom- 
pressible, so that c is zero and A is infinitely large, p remaining finite ; 
this, of course, leads to the fourth equation — 

du , dv , dw n 

^T + ^ + ^ = ^ .... (18) 

And from these equations the equation to the surface of wave slowness is 
shown to be 

— -1 ^-1 _-l 

a2 h^ c^ 

This, however, is not Fresnel's surface, and experiments of a very 
high ' degree of accuracy have shown that the wave surface in a 
•crystal is very approximately indeed Fresnel's surface, and of course 
this is fatal. But, as we shall see in the next section, according to all the 
theories yet proposed based on the mutual reaction between matter and 
•ether, the first and most important effect of the matter is to alter the 
apparent density of the ether in the way here supposed. The mutual 

72 

reaction, it can be shown, will introduce terms of the form Jc —^ into the 

dt^ 
equations, and k may conceivably depend on the direction. 

§ 14. Equations of motion practically the same as Lord Rayleigh's 
are given by Boussinesq, Lommel, Ketteler, and Voigt, and the question 
arises. Are these equations incompatible with Fresnel's wave surface ? 
Lord Rayleigh has, of course, proved that they are if the equation 

du dv div ^ 

dx dy dz 

•expresses an absolutely necessary condition ; but it is not difficult to show 
that if, instead of the above equation, we put 

1 ^w J. (^ 1 du „ 

a^ di b^ d^ '^ dz ~ ' ' ' ^ -^ 

then the wave surface will be Fresnel's, the direction of vibration will be 
normal to the ray, and will be in the plane containing the ray, the wave 
normal, and an axis of the section of the ellipsoid a^x"^ + I'^if + c^^^ = i 
by the wave front, and while the velocity of propagation will be inversely 
proportional to the length of this axis. 

Assuming equations of the same form as Lord Rayleigh's (17), we have 
to determine the pressural wave given by p —p^ti(ix+my+nz-\e) ^.j^g equation 

■where ti = \Q^^Klx+my + ,iz-Yl), gtg_^ 

and this, on Lord Rayleigh's assumption of Ik + mu + wr = 0, reduces to 

Po = «B0oV^{^, + ^^ + ^y} . . . (21) 

• See Stokes, Proc. Roy. Soc. vol. sx. p. 44B ; Abria, Ann... de Chhnie; Glazebrook 
riitl. Trans. Pt. I. 1879 ; Kohlrausch, Wied. Ann. t. vi. p. 86 ; t. vii. p. 427. 

n2 



180 REPORT — 1885. 

while, on the hypothesis suggested above, we should find 

po=-iBdQ{\l + lum + rn} .... (22) 

The theory as here modified would, it appears to me, agree in its results 
with all the experimental facts ; the main difiiculty lies in the assumption 

of equations of the form—. — =— ^ + V ^u for the medium when it is not 
^ a''' at B ax 

strictly incompressible. The value of 2^ is generally A|-— + -=- +_— j, 

and the introduction of « is based on the supposition that - — | + -- 

ax ay dz 

is zero, and A infinite ; it is questionable if the substitution ought to be 

made, except in this case. 

§ 15. Kirchhoff 's paper on double refraction ' was read before the 

Royal Academy of Berlin, and is contained in their ' Transactions ; ' its 

more important part deals with the problem of reflexion and refraction. 

So far as the double refraction is concerned, it does not differ in any 

important points from Neumann's theory. The medium is supposed to be 

incompressible, so that -{- — + — - vanishes, but the coefficient of this 

ax ay dz 

expression is treated as finite, and the terms involving it in the ex- 

pi'ession for the energy are omitted. The criticisms on Neumann's theory, 

contained in Professor Stokes's report, apply again here. 

Chapter II. — Dispersion of Light. 

In 1870 Ketteler ^ published a paper on dispersion, which forms the 
first of his important series on that subject. He commences with an 
account of Cauchy's theory and the various modifications which have 
been proposed. 

§ 1. Redtenbacker ^ had considered the problem under the supposition 
that each matter molecule is surrounded by an ether shell, and obtained 
the formula 

J- = a+^+c\2 (23) 

\ being the wave length in the medium, and /x the refractive index. 

§ 2. Christoffel,^ discussing Cauchy's formula, already mentioned,' viz. 

1 ^ i ^ 

had shown that, while a and h may be considerable in value, the 
other constants decrease rapidly. This two-constant formula may be 
written — 

/^= .-, ■ /°^^.. r. • • . (24) 



I 
I 



v/0-^")V('-x')' 



' Kirchhoff, Ahhandl. der Konigl. Ahid. zu Berlin, 1876. 

2 Ketteler, ' On the Influence of Ponderable Molecules on the Dispersion of Light, 
and the Signification of the Constants of the Dispersion Formulae,' Poffff. Ann, 
t. cxl. p. 1. 

^ Kedtenbacker, Bi/namiden-Si/stem, Mannheim, 1857. 

■• ChristofEel, Fogg. Ann. t. csvii. * See p. 165. 



ON OPTICAL THEORIES. 181 

Thus /uq and Xq are the refractive index and wave length for the shortest 
waves transmitted, and /itov/^the refractive index for the largest possible 
waves. 

§ 3. The various theories are then compared with experiment, by 
Ketteler, and it is shown that the formula 

i,=KX>+A + g^.O .... (25) 

represents the results of the comparison most accurately. This formula 
was obtained by Briot, working on the same lines as Redtenbacker, but he 
supposes the coefficient K, which he shows depends on the direct action 
between matter and ether, to vanish. Van der WilHgen ' also called 
attention to the importance of the term in X^, but could not account for 
its existence. Ketteler, following Briot, then analyses the manner in 
which these various terms arise, and shows that the force on any 
vibrating ether particle may be written 



X2 



< Displacement of particle > 

x{(, + /0(l-L)-^%f+^X^} 



This, of course, gives 

-l=A + g + KX2 (26) 

The term in g + h arises from the mutual reactions of the ether particles, 
supposed to be uniformly distributed. If the action of the matter be 
simply to produce a periodic variation in the density of the ether, the 
terms in L and M are introduced, while the term involving gi + h^ 
comes from a direct force expressed by mm^rf^{r) between the ether 
and matter particles wi and wij respectively. If we put rf^(r) = n/r", 
then the value of gi + 7i, is —^(n — 2)'Sim^fi/r"'^^. 

Briot supposes that the term KX^, to which this gives rise, is not 
requix-ed by the experimental results, and therefore puts w=2. Ketteler, 
however, shows that this term must be included. 

Holtzmann and C. Neumann had already insisted on the importance 
of retaining in the equations terms to express this direct action, and 
Neumann gives as the expression in an isotropic medium for the force 
arising from a displacement ti, 

Cu + C ^ + C" i^. 

But the theory of dispersion in its complete form requires that thu 
motion of the matter particles should also be included. This is treated 
of in the next section of the Report.^ 

A problem closely connected with dispersion is the relation between 
the refractive index and the density of a medium. This has been dealt 
with experimentally by various physicists, notably by Gladstone and Dale 
in England, and Ketteler in Germany. 

§ 4. L. Lorenz ^ has recently developed the theory of the transmission 

' Van der Willigen, Archives du Muue Teyler. - See p. 213, etc. 

^ L. Lorenz, ' On the Refraction Constant,' WieA. Ann. t. xi. 



182 KEPOBT— 188/5. 

of light through a medium consisting of a series of small spheres im- 
bedded in the ether. The velocity of light in the interspaces is the same 
as in free space, and the wave length is supposed to be great compared 
with the intei'molecular distances. It is assumed, then, that the disturb- 
ance u at any point may be written u= (t(Q + u<,)C + UiS, where the 
average values of 1*1 and «.> over the space containing some considerable 
number of molecules are zero, and C and S are written for the sine and 
cosine of kt — Ix — mij — nz — c. From this it follows that, if /z be the refrac- 

tive index and d the density, - ^ — _ is proportional to d.* 

The paper is followed by one by Lorenz and K. Prytz, giving the 
results of an elaborate series of observations which show a close agree- 
ment between this expression and experiment. 

Chapter III. — Aberration and Phenomena connected with the Motion 
OP THE Medium through which Light is being propagated. 

§ 1. The aberration of light on the undulatory theory was accounted 
for by Fresnel • on the supposition that a moving body of refractive 
index fi carries with it a quantity of ether of density fi^ — l, the density in 
a vacuum being unity, while light is propagated through this ether, part 
of which is at rest and part mo^ang with a velocity v (that of the body), 
as if the whole were moving with the velocity (I— /i~')t;. 

The experiments of Fizeau^ on the displacement of the fringes of 
interference by a moving medium led to a result in close accordance with 
this theory, 

§ 2. A more general and simpler proof than the one published by 
Fresnel of the fact that this leads to the ordinary laws of reflexion and 
refraction was given by Professor Stokes in 1846.^ 

In this paper Professor Stokes points out that the same result as to 
the velocity of light in the medium will be arrived at if we suppose the 
ether on entering the medium to be condensed, and on leaving it to be 
rarified, while the whole ether in the body travels with the velocity given 
above ; for, if we take two planes, one outside the other inside themedium^ 
each moving with the A^elocity v normal to itself, the quantity of ether 
which crosses the two planes per unit time will be the same, and hence, 
if V be the velocity of the ether in the medium, then we have, since the 
densities are 1 and fi^ respectively, 

and hence Y M^""-'- 



Moreover, this comes to the same thing as supposing the medium to be at 
rest, while the ether outside moves with a velocity v, and that inside 
with a velocity?;/^-. The direction of a ray is shown to be that in which 
the same jDortion of a wave moves, moving relatively to the medium, and is 
found by drawing from a given point a line of length V//i in a direction 

* Compare this with a similar paper by H. A. Lorenz, p. 255. 
' Fresnel, Anvales de Chimie, t. ix. p. 57. 
- Fizeau, Annates de Chimie (3), t. Ivii. p. 385. 

' Stokes, ' On Fresnel's Theory of the Aberration of Light,' Phil. Mag. vol. xxviii. 
p. 76; Afatheviatical Pajjcrs, vol. i. p. 141. 



ON OPTICAL THEOEIES. 183 

normal to the wave, and from the extremity of this line a second of length 
v/f.i^ in the direction of motion of the ether; the ray is the line joinino- 
the first point to the extremity of this second line. The velocity of the 
ether is resolved into its components perpendicular and parallel to the 
reflecting sui'face, and the effect of each component is considered ; it 
is shown that rays are reflected and refracted according to the ordinary 
law of sines. 

§ 3. But in a paper six months previously Professor Stokes ' had 
considered the problem in a much more general manner. He supposes 
that the earth and planets carry with them a portion of the ether sur- 
rounding them, so that close to their surfaces the ether is relatively at 
rest, while the velocity alters as we recede from the surfaces until, at no 
great distance, it is at rest in space. 

The direction in which a body is seen is normal to the waves which 
have reached the observer from the body, and the change in this apparent 
direction which arises from the motion of the ether is investigated. 

The axis of z is taken in the direction of the normal to the undisturbed 
wave, and a, f3, y are the angles which the normal to the actual wave 
makes with the axes ; u, v, w are the velocities of the ether at a point 
X, y, z at time t ; V the velocity of light. The equation to the wave is 

^ = C + Vi + c, 

i being a small function of x, y and t. 

Then, by considering the displacement of the extremity of an element 
Ylt, drawn normal to the wave, it is shown that at time t + Zt the equa- 
tion is 

z = G + Yt + ^ + {lo + Y) dt, 

and hence we see that 

dZ_ 



, -w. 
At 



From this we find- 
If now 



IT 1 [dw 7 ,T TT 1 [dw , 



dio du dw dv 

dx dz dy dz 

so that udx + vdy + wdz is a complete differential, then 

«2 — "l = "vT- > P2 — P\ = 



w.,-zt, -; _ T _ ^'2 - ^1 



and these equations, it is easily seen, imply the known law of aberration. 
In an additional note it is shown that if aj, /3i be the inclinations of 
a ray at any time to the axes, then 

fdiij dw\ -. \ 

^^^=\jz-'d^Y' 



j,i f dv dw \ T. 
\az ay J 



(27) 



' Stokes, 'On the Aberration of Light,' Phil. May. vol. xxvii. p. 9 (July, 1845) • 
Mathematical Pampers, vol. i. p. 134. ' 



184 KEPOBT— 1.S85. 

So that, i{ vdx + vdy + ivclz be a comjDlete differential, Jctj and dj3i both 
vanish, and the path of the ray is a straight line. 

Thus, if the motion of the ether produced by the passage of the trans- 
parent medium through it have a velocity potential, all the phenomena 
of aberration will be such as are actually observed. The important ques- 
tion as to whether such a motion is probable in the ether is discussed in 
another paper. • 

§ 4. Professor Stokes's views on the constitution of the ether are given 
in his well-known paper on fluid friction.^ He distinguishes there between 
the properties of rigidity and plasticity, pointing out that an elastic solid 
may under different external conditions become a viscous fluid, while 
the gradation between viscous and perfect fluids is quite regular. There 
seems, then, a probability that the property of rigidity will run to some 
extent through the whole series, becoming, in the case of fluids, masked 
by some other more important property. The mobility of a fluid is the 
limiting case of great plasticity ; but even a perfect fluid may admit of 
a finite, though extremely small, amount of constraint of the nature of 
shearing stress before being relieved from its state of strain by its mole- 
cules assuming new positions of equilibrium. A consideration of the 
length of a wave in light motion — about '00003 inches — renders it pro- 
bable that ' the relative displacement of the ether particles may be so small 
as not to reach, or even come near, the greatest relative displacement 
which could exist without the molecules of the medium assuming new 
positions of equilibrium.' 

These same views also tend to confirm the belief that for fluids, and 
among them the ether, the ratio of A to B (the elastic constants of the 
medium in Green's notation) will be extremely great. 

We are led, then, to conclude that, in considering the motion set up 
in the ether by a moving body such as the earth, we may treat the 
ether as an incompressible fluid, while, on the other hand, when 
dealing with the extremely small disturbance produced by the passage of 
a light-wave the rigidity of the ether may come into consideration, and 
the equations required will be those of an elastic solid. In the first case 
any tangential forces which may arise, if the fluidity be not perfect, will 
depend on the relative velocities of the parts of the fluid ; in the second 
case such tangential forces will depend on the relative displacements of 
those parts. In the paper in the ' Philosophical Magazine ' for 1846 
Professor Stokes shows that it is probable that a velocity potential will 
exist unless the action of the air on the ether be such as to prevent it, 
and, further, that it is improbable that the air will so act. 

For suppose a sphere started from rest in such a medium, and then 
after a short interval stopped for a time, then started, and so on . 

The initial motion will have a velocity potential, and if the fluid 
were perfect this would continue, so that reducing the sphere to rest 
would stop the motion everywhere. But the motion with the velocity 
potential is shown to be unstable, and hence there is left in the neigh- 
bourhood of the sphere a small outstanding disturbance. This is carried 

' Stokes, ' On the Constitution of tlie Luminiferous Ether viewed with reference 
to the Phenomenon of the Aberration of Liglit,' Phil. Mag. vol. xxix. p. 6 ; Math, aiid 
Phys. Papers, i. p. 15.3. 

* Stokes, ' On the Theories of the Internal Friction of Fluids in Motion, and the 
Equilibrium and Motion of Elastic Solids,' Trans. Cavib. Phil. Soc. vol. viii. p. 287; 
MatJi. and Phys. Papers, i. p. 75. 



ON OPTICAL THEORIES. 185 

off with the velocity of light, which is about 10,000 times as great as 
that of the earth, so that at the end of the second interval the ether near 
the sphere is at rest again and the same effect is repeated. It seems, 
therefore, probable that there will be a tendency to set up a motion in 
the ether not having a velocity potential, but that the beginnings of such 
motion will be propagated away into space at a very great rate, and that 
the actual motion will satisfy the condition that udx + vdy + wdz is an 
exact differential. 

In a subsequent paper Professor Stokes gives the solution of the 
equations of motion of a sphere moving in a viscous fluid, and then 
proves that when the fluid becomes perfect the motion becomes unstable, 
so that udx+vdy + xodz is not a complete differential ; but if the tangential 
force depends, not on the relative velocities, but on the relative displace- 
ments of the molecules — that is, if for the beginnings of the variation from 
irrotational motion we must consider the rigidity of the ether (?".e , in 
our mathematics use the equations of an elastic solid) — then, as shown 
already, this nascent variation from irrotational motion will be propagated 
away by transverse vibrations, which, however, do not produce optical 
effects, either because they are too feeble or because they are discon- 
tinuous, or, if continuous, because their period falls outside that of the 
visible spectrum. 

Or, to put it slightly diffei-ently, if the fluid has any very slight 
rigidity, a given arrangement of its parts is not necessarily one of equi- 
librium. Suppose, then, the fluid displaced from rest by the sudden 
motion of the solid, and that after a short interval the solid is stopped, 
the velocity of the fluid will be reduced everywhere to zero, but the 
resulting configuration will not necessarily be one of equilibrium, and the 
motion arising from this slight strain will be set up. 

Thus, without making Fresnel's somewhat violent assumptions as 
to the relation between the ether within and without a transparent body, 
a perfectly reasonable and consistent account can be given of aberration 
depending only on the irrotational character of the motion induced by the 
moving body in the surrounding fluid. Unfortunately, as Professor Stokes 
points out, we have as yet no experiments competent to decide between 
the two, and he does not see how such experiments could be devised. 

§ 5. Ketteler is the author of a long series of papers connected with 
the subject of aberration, which have appeared in Poggendorff's ' Annalen.' 
The last of these ' contains a summary of the results of the whole. 
The problem of reflexion and refraction at a moving surface is con- 
sidered, and it is shown that the intensities of the reflected and refracted 
rays will not be modified by the motion if the vibrations be at right 
angles to the plane of polarisation, as Fresnel supposed. 

§ 6. The papers also deal with the problem of the emission of light 
from a moving source, and the principle first enunciated by Doppler,^ in 
consequence of which it follows that if the source and receptacle approach 
each other in time ^ by a space equal to n times the wave length in the 
medium between the two, then the receptacle receives in that time n 
more vibrations than it would if the two were relatively at rest ; and if 
this number be N, the apparent frequency is increased in the ratio N -)- «. 

' Ketteler, ' Ueber den Einfluss der astronomischen Bewegungen auf die optisch n 
Erscheinungen,' Pt. VI., Pogg. A^m. t. cxlvii. 

^ Doppler, Lasfarhige Licht der Dojjpel- Sterne. 1842. 



186 EEPOBT— 1885. 

to N, or if V be the velocity of light, v that of the source towards the 
receptacle, in the ratio Y + v to V. 

This principle has been considered by other writers, among them 
Petzval, Von Ettingshausen, Klinkerfuess,' Van der Willigen,^ and 
Seccbi,^ and an interesting discussion of their work has been lately 
given by H. H. Turner, in a dissertation for a fellowship at Trinity 
College, Cambridge. 

Chapter IV. — Reflexion and Refraction. 

§ 1. The various theories of reflexion and refraction advanced by 
Fresnel, Green, MacCullagh, Neumann, and Cauchy have been discussed 
by several writers, and attempts have been made to reconcile them with 
the experiments of Jamin, Quincke, and others. Jamin was the first to 
show that by reflexion at most transparent media plane polarised light 
becomes elliptically polarised, and that this elliptic polarisation is most 
marked when the angle of incidence does not difier much from tan -'//. 
Moreover, for some substances for which the refractive index is greater 
than 1-4 the phase of the component in the plane of incidence is re- 
tarded relatively to that at right angles to the plane, while if the index be 
less than 1'4 the reverse is the case. 

The original theories of Fresnel and MacCullagh do not in any way 
explain this phenomenon, and are therefore incomplete. 

§ 2. Cornu'* has discussed the application of Fresnel's theory 
to crystals, and has suggested a means of explaining the apparent 
discontinuity of the displacement normal to the surface to which that 
theory leads. The explanation— which Professor Stokes has been in 
the habit of giving, independently of Corna, in his lectures at Cambridge — 
rests on the fact that the density of the ether is different in the two media. 
If, then, we take two planes in the two media parallel to the interface 
and at a small distance apart, the quantity of ether between the two 
planes remains the same ; hence, if u, u' be the displacements normal to the 
planes, and p, p' the densities, the equation of continuity gives pu= p'v! , 
and this is the condition assumed by Cornu in his papers. This con- 
dition, combined with those of the continuity of the displacement parallel 
to the surface, is consistent with the equation expressing the conservation 
of energy. 

The correctness of this condition depends on the view we take of the 
ether in the two contiguous media. If the two portions of ether be 
treated as two separate elastic solids in contact over a common surface, 
then over that surface the displacement must be the same in the two 
media ; but the equality of the displacement normal to the surface cannot 
extend beyond a very small distance within the medium, and in the dis- 
placement is included that which comes from the pressural wave, as well 
as that which produces light. During the motion, of course, the bounding 
surface of the two media does not remain plane, but is a curved surface,, 
the co-ordinates of any point on which at time i are w, -y + i/, w + z. 

' Klinkerfuess, Astronomische Kachrichten, t. Ixv. p. 17, t. Isvi. p. 337. 
"^ Van der Willigen, Archives du Musee Teijler, t. iii. p. 306. 
' Secchi, C. R. t. Ixxxii. p. 761, t. Ixsxiii. p. 117. 

* Cornu, ' Eecherches sur la reflexion crystalline,' Ann. de Chim. (4), t. xi. 
p. 283. 



ON OPTICAL THEOKIES. 187 

The condition of no dilatation holds throughout both media, and the 
stresses over the surface are the same in the two. 

According to this view, a small portion of ether which belongs to one 
of the two media remains of unchanged density, and always forms part 
of the same medium. 

We may, however, consider the question somewhat differently, and look 
upon the ether in the two media as continuous, but of different densities 
on the two sides of the interface. A portion of ether belonging to the 
first medium may cross the interface and become part of the second, and 
in so doing its density is changed. There will thus be a thin sheet of 
ether lying over the interface in which rapid periodic changes of density 
are occurring. 

If, then, we consider the motion on the two sides of the sheet, we 
have for its determination the fact that the quantity of matter within the 
sheet is constant, and therefore that puz=zf)'u\ while the motion parallel to 
this sheet will ultimately be the same in the two media, and the energy 
in the reflected and refracted waves will be equal to that in the incident. 
But this condition pu=p'u' does not hold within the sheet where the 
variations of density are taking place, and where the effects of the 
pressural wave are appreciable. The motions denoted by m and u' are 
light-motions, exclusive of those which give rise solely to the pressural 
wave. Moreover, it is supposed that this layer of variable density is so' 
thin that the phase of the distui-bance may be treated as the same over 
its two bounding surfaces. It is further assumed that the above are the 
only conditions which hold at the surface, and these can be satisfied 
without supposing any change of phase to arise from the reflexion. As a 
fact, there are other conditions involved in the equality of the stresses 
over the surface, and to satisfy these it is necessary to suppose that when 
the vibrations are in the plane of incidence the phases of the incident 
reflected and refracted waves difier even at the surface. 

To assume Fresnel's conditions, as is done by Cornu, without change 
of phase is equivalent to supposing that this sheet of variable density is 
indefinitely thin when compared with the wave length of light. 

Green himself considered the effect of supposing tlie change in 
refractive index to take place in a gradual manner, replacing the refract- 
ing surface by a regular series of layers, of indices Hu fx^, etc., each of 
thickness t ; and proved that the effect of such a series would be to make 
the intensity of the reflected wave more nearly that given by Fresnel's 
tangent formula. 

The effects of supposing the change of properties from one medium to 
the other to be gradual was discussed by L. Lorenz in the year 1860. 

§ 3. In his first paper • he supposes that Fresnel's formute express 
the result of a sudden transition, and investigates how they must be 
modified if the transition be gradual. The variable sheet is divided into 
a series of layers, each of constant density. A ray reflected at one of the 
interior layers will on emergence be retarded relatively to the ray 
reflected at the surface. Let I be the retardation of the ray reflected at 
a layer on which the angle of incidence is x, and let a, ft be the angles of 
incidence and emergence, then the disturbances in the reflected ray are 
shown to be : — 

,r j-^; ^o^^'^^' ' On the Eeflexion of Light at the Bounding Surface of two Isotropic 
Media,' Pogg. A^m. t. cxi. p. 460. ^ 



188 REPORT — 1885. 

(1) Light polarised in the plane of incidence — 

R = A s^" (" - /^) fcos kt + tan A sin ht\ . . (28) 

sin(a + /3)L J 



where 



. sin O cos a P/ o n i. ■ o -, , \dS , /-nrw 

tan A = -r-75 . - , ( COS'' p tan a; — sin- p cot j; )-dx- . (29) 

sm'' a — sm^ p}a\ J dx 

(2) Light polarised at right angles to the plane of incidence — 

R' = - A' ta n (a - ft ) V^^ ^^ + tan A ' sin kt\ . (30) 

tan (a + /5) L J 

2a sin 2/3 f^r sin 2x _ sin 2ft~\dc -. .o-i >, 

a - sin2"2/3jl "^1^2/3 '^^^x \ dx ' ^^ 



where 



, , , sin 2fi 

tan A' =^2-0- 



7^ 

Now -- is always small, hence A is small ; but for sin 2a = sin 2/3, 
ax 

or tan a = ft, tan A ' is infinite. 

Jamin's results as to positive and negative reflexion are shown to 
follow, and if it be assumed that the density is approximately proportional 
to/ii* — 1, the thickness of the variable sheet can be estimated, and is found 
to lie between ^L and -j-^^ of the wave length. 

In criticising this theory. Lord Rayleigh, in a paper we shall shortly 
consider, has pointed out that Fresnel's tangent formula does not express 
the result of sudden transition, and that Green's formula, which does, 
deviates from the truth on the other side. On the electro-magnetic 
theory, however, the tangent formula is strictly true, and Lorenz's 
investigations regain their interest. 

Another objection which Lord Rayleigh has made to the supposition 
of gradual transition, however, may be a serious one. It is that there 
should be some indication of colour in the light reflected near the polaris- 
ing angle, since it is to all intents and purposes a case of interference 
produced by a thin plate. It may, however, happen that the thickness of 
the plate is comparable with that of the black spot in Newton's rings, 
and so, though big enough to modify the quantity of light reflected, is too 
small to show colour. According to Newton, the thickness of the black 
spot in a soap film is about Jo of a wave length, while Reinold and 
Riicker have recently determined it as -g^^, and these fall within the 
limits required by Lorenz to explain the variations from Fresnel's tangent 
formula. 

In another paper ' the problem of reflexion at a surface across which 
the density varies gradually has been more fully considered by Lorenz, 
and the surface conditions on either side of the variable layer are deduced 
according to a strict elastic solid theory, and lead to similar conclusions. 

§ 4. Cauchy gave the results of his theory of reflexion and refraction 
without the calculations which were supplied by Briot * in France, and 
Beer ^ and Eisenlohr '' in Germany. 

' L. Lorenz, Poffg. Ann. t. cxiv. p. 238. 

'^ Briot, Liom-iUe's Journal, t. xi. p. 305 ; t. xii. p. 185. 

' Beer, Fogg. Ann. t. xci. and xcii. 

* Eisenlohr, Fogg. Ann. t. civ. p. 346. 



ON OPTICAL THEORIES. 189 

An account of the various theories is also given iu papers by Lord 
Rayleigb,' with a careful criticism and comparison of them all. 

In the first part of this paper Lord Rayleigh discusses fully the 
difference between the theories of Green and MacCullagh, and develops 
completely the consequences of the latter, taking into account the full 
effect of the pressural wave. This had been done first by Lorenz in the 
paper already referred to, and he showed that the results to which 
MacCuUagh's theory leads are totally inconsistent with experiment. 

Lord Rayleigh points out that the fundamental assumptions of Green 
and Fresnel amount to assuming an identity between the statical pro- 
perties of the two media, while the dynamical pi-operties depending on 
variation of density are different ; while, moreover, as we have seen 
already, Cauchy's surface conditions, founded on the principle of the 
continuity of the displacements and their differential coefficients with 
reference to the normal, though erroneous if we suppose the rigidity of 
the ether different in the two media, become identical with Green's if 
we adopt his fundamental hypothesis. The real difference between Green 
and Cauchy lies in their respective treatments of the pressural waves. 

The true surface conditions lead to the folio wins: results : — 

Let I, T], i^ be the displacements, n the rigidity, m the second 
coefficient, such that m + n is the A of Green's papers, and D the 
density, while g^ = (m + n) jD, y- = ?i/D for the one medium. 

Let a; = be the bounding surface, and let the axis of z be parallel to 
the front of the waves. And suppose/, F, and/i to represent the incident 
reflected and refracted waves, while f and ((>' are the angles of incidence 
and refraction. 

Then, for vibrations normal to the plane of incidence — 

tan f' n'\ 



F' tan (p n 



(32) 



f tan (p' i 

tan <i> 1 
and this becomes : — 

Case I. n = n' (Green, Fresnel, Cauchy) — 

F^ _ sin (f - f) 

f 8in(f + ^) • • • • ^'i^) 

Case II D = D' (MacCullagh, Neumann)— 

F_ tan((^^-0) 

/ tan (f + ^) • • • • ^''*^ 

Now, Jamin, Quincke, and others have shown that this latter formula 
is not strictly true, and hence at this point the evidence is already in 
favour of Fresnel's hypothesis. 

Turning now to the case of the vibrations in the plane of incidence, put. 

dx dij 
_ d^_d'^ 

dy dx 

' J. W. Strutt, ' On the Reflexion of Light from Transparent Matter,' Phil. Mag. 
August 1871 ; ' On the Reflexion and Refraction of Light by Intensely Opaque- 
Matter,' Phil. Maj. May, 1872 o j j f"^ 



(35) 



190 REPORT — 1885. 

Then ^ refers to tlie light wave and $ to the pressural wave ; let *' 
refer to the incident wave, *" to the reflected, ^, to the refracted, so that 

Tlr __ \p'gHa.T + l!i + cO r ijf//gt(-ax + 6i/ + ct) 

etc. Then the surface conditions become in general, if we put 
^/ ^ y^U _ X, ^' - ^" = Y. 

i(«> + a)!) =*i - X 
6(* — <I>i) = aY — a,^i 

4.{m(a'2 + i^) - ^nb^} + ^nabY 

=<I)i {)«'(ai'2 + ^2) _ 2n'b''} + 2n'a,b^i . . (36) 

n{b''^i- a^X + i-&(«Y - «,^,)} 

= «' {^^X - a, 24', + ^•Z;(«Y - a,^,)} • • (37) 

MacCullagh, in his original work, neglects the pressural waves en- 
tirely, and pats $ = <t, = 0, dei'iving his result (Fresnel's sine formula) 
from equation (35). These results are inconsistent with (36) and (37), 
and therefore wrong. To obtain the correct solution we must remember 
that m is infinitely great, while a'^ + h^ is vanishingly small, and m(a'^ + b^) 
= Dc^. This is what has been done by Green, and applied by Lorenz 
and Lord Rayleigh to MacCullagh's theory. 

[Cauchy puts o.'^ + 6^ = —k"^. We shall consider the consequences 
of this shortly.] 

Hence (36) becomes 

D* - D'*i = -^(/i - n') — ' -. , \ ' (o8) 

c^ l ^ I 

Cask I. n = n' (Green). 
Then 

W-Ji tan (<p - <!>') f 1 + M' tan" (<p + <!>') ) * .gg. 

tan (<!> + (l>')\l + M2 tan* (f - ff,')) ' ' ^ ■> 

W and R being the amplitudes of the reflected and refracted waves, and 

2 "I 

M eaual to ^- , while the diSerence of phase between the incident 

^ 1^^ + 1 

and refracted waves is e where 

cot e = L cot (<}>- (p>) . . . . (40) 
while between the reflected and refracted waves it is e', where 

cot e' = ^ cot (r/, +i>') . . . . (41) 

Case II. D = D' (MacCullagh's corrected theory). 

The equations are very complicated and lead, when the difference in 
the rigidities is very small, to two polarising angles of 22^° and Q'7^° 
respectively, results which are thus utterly at variance with experiments. 

Cauchy's theory leads to results the same in form as Green's, if we 
substitute — £ sin for M, e being a certain small constant. 

The solution is contained in the above equations if we tabe 

a'2 + b^= - l\ a,'2 + b-'=- t,^ 



ON OPTICAL THEORIES. 191 

and put 

27r/l 1 N 

T{k-kJ = -' • ■ . . (42) 

In Eisenlohr's account of Cauchy's work it is assumed at first that 
the normal waves travel with the same velocity as the transverse, and 
then the solution is modified by putting for X^^, \", the wave lengths of the 
normal waves, the values — l,,l/ — 1 and — Z'V — 1. This modifies 
tpii and ^", the angles of refraction and reflexion of the normal waves, so 
that their sines become imaginary, while cos ^^^ is real and negative, 
cos 0" real and positive. 

A difierence of phase is thus produced, determined by the following 
•equations : — 

tan e = p tan (^ — 0'), 



where 
and 



tan e'=^ tan (^ + f'), 
V = 



m."viii — l' 



Jamin's results show that^ is very small ; hence we may write 

where u is small, and then 

2m sin (f> 

^ ~ tVTt^ + sin^ 0) • • • . (43) 

Cauchy puts p = e sin f, when e is a small constant. Hence we must 
suppose that t is great compared with f. 

Lorenz and Lord Rayleigh have both pointed out the serious obiec- 
}^^ *'° «*" "'^'^^ *° ^^^ *^®°^y ^° *^^s fo^"^- The equation to determine * is 
d^ df '^W medium will be essentially unstable. 

Moreover, if Z; be a constant, e varies inversely as X, and chromatic effects 
, near the polarising angle should be much more marked than they are 
I 1 have, however, given an account of Eisenlohr's paper mainly because 

ot another suggestion he makes, which renders it very nearly identical 

with Green s. He suggests that the normal or preesural waves mav 
' vanish by a sort of total reflexion, their velocity being very great com 
, pared with that of the transverse waves.' So that we have X , and X" 

very large instead of imaginary, and from this he finds 

_ \,^ - X"^ 
^ X ^ + \"2 ("^^ 

This vanishing by a sort of total reflexion is exactly Green's theory, for 



192 REPORT — 1885. 

if x' be the angle of refraction for a normal wave produced by a trans- 
verse wave incident at an angle <j>, then, with the notation of Lord Ray- 
leigh's paper, 71 sin^ x = ™ sin^ ^, and hence x is iniaginary unless (p is 
less than sin"'(n/?u). That is to say, if wt be infinitely large, the effects 
of the pressural wave are entirely confined to the surface, and, indeed, 
for this total reflexion, if we may so call it, of the pressural wave to 
take place, it is practically not necessary for the ratio of n to m to b© 
zero. If, for example, n/iu = 1/100, there will be total reflexion if f is 
greater than 0° 85', and for so small an angle of incidence as this the 
component of the vibration normal to the surface on which the pressural 
wave depends would be too small to produce a measurable efiect on the 
transmitted light. 

If we put \^JX" = f.iQ, then jJq is the refractive index of the medium 
for the normal vibrations, and we have for ^j 



p-':^^ (^5> 

Ho 



' + 1 



Now, it was shown, first by Haughton,' and then by Kurz, that the 
expressions (39-41) agree with experiment very closely if M or p be 
treated as a constant to be determined by experiment, and if we suppose 
p to have the form just given, then for sulphuret of arsenic, for which 
fi = 2-454, according to Jamin, ^Iq = TOSS. Green, going further into the 
mechanism of the motion, has shown, however, that on a strict elastic 
sohd theory we must have \,J\" = \/\' and fJo^h'- The last conclusion 
Eisenlohr calls ' durchaus unhaltbar,' and in this he is right if he means, 
that it does not agree with experiment, but wrong if he means that there 
is a flaw in Green's theory. The suggestion that ^ and /iq may be 
diff'erent is due to Haughton,^ but the reasons he has assigned for it have 
been shown by Eisenlohr to be invalid. Lord Rayleigh has suggested 
others which have great weight, and the importance of which will be 
more clearly seen when we come to consider some recent theories based 
on the mutual reaction between matter and the ether. The large quan- 
tities m and m' are, in Lord Rayleigh's paper, eliminated from the equa- 
tions by means of the relations 

viia'^ + h"") =Dc2, 

D and D' being the densities of the ether in the two media. 

Now, in the pressural wave we are only concerned with a layer of 
ether close to the bounding surface, and Lord Rayleigh's suggestion is 
that, although the transverse vibrations are affected nearly in the same 
way as if the transition were instantaneous, it may not be so for the 
surface waves, and that therefore we may put D/D' =yuo^ where /uq is less 
than fj. There are, I think, even stronger reasons for supposing /.iq and 
^ to be difierent to be derived from the theory I have already referred 
to, which will be developed later. 

Thus the papers of Lord Rayleigh, Lorenz, and Eisenlohr show, con- 
clusively, that Neumann and MacCullagh's theory is inadmissible, and 
that Green's strict elastic solid theory, when slightly modified in a per- 

' Haughton, Phil. 3/aff. (S. 4), vol. vi. p. 81 ; Kurz, Pog/;. Ann. t. cviii. 

2 Haughton, Phil. Mag. (S. 4), vol.vi. p. 81 ; Eisenlohr, Pugg. Ann. t. civ p. 3t6. 



ON OPTICAL THEOEIES. 193 

fecfcly reasonable way, leads to results agreeing very closely with experi- 
ment, while Canchy's method of treating the pressural wave requires 
an unstable condition in the ether. 

In another paper Lord Rayleigh ^ considers the problem of reflexion at 
the confines of a medium of variable density. The incidence is supposed 
to be normal, and in, the particular problem solved completely, the density 
is supposed to vary as the inverse square of the distance from a fixed plane 
parallel to the surface. This variable medium extends between the two 
planes x = x^^, a; = a'2, and the density is constant on the other sides of 
these planes, and it is shown that if the thickness of the variable layer is 
not very different from the difference in the wave lengths in the two, then, 
for the case in which the two media are air and glass, the reflexion will 
be excessively small. 

§ 5. The paper by KirchhoS"- in which the problem of reflexion and 
refraction is considered has been already referred to. The theory there 
given is, in its results, nearly the same as those of Neumann and 
MacCullagh. 

The ether is not treated strictly as incompressible, though it is 
supposed that only transverse waves are propagated, and therefore that 
the equation 

du dv dw /N 

dx d)j dz 

is satisfied without the coefficient A becoming very large. These trans- 
verse waves falling on the interface of the two media would tend to set 
up longitudinal vibi-ations. Some surface action, however, is supposed to 
go on over the interface, the result of which is to quench these vibrations 
and the condition that this surface action should involve neither loss nor 
gain if energy is formed. This, with the three equations implied in the 
continuity of the displacement, makes four conditions from which the 
intensities and planes of polarisation of the reflected and refracted waves 
can be found. 

The theory differs from MacCullagh's merely in recognising the 
possibility of the existence of the normal waves, and then accounting for 
their absence by means of some unknown surface action. It is not a strict 
elastic solid theory, nor does it attempt to explain of what nature the 
surface forces are which quench the normal waves. The formulas to 
which it leads are identical with MacCullagh's,' and do not offer any 
explanation of the change of phase observed by Jamin. It can hardly 
be looked upon, therefore, as a satisfactory explanation of the phenomena, 
nor can we regard Kirchhoff's principle, as the fundamental hypothesis 
is called by various German'* writers, as one which may replace the true 
surfece conditions of an elastic solid. 

Chapter V. — Metallic Reflexion. 

§ 1. Various experimenters — and among them Brewster, MacCullagh, 
Briot, Airy, Neumann, De Senarmont, Jamin, Quincke, Wernicke, and 
Conroy — have investigated the optical efl'ects produced by metallic re- 

' Lord Eayleigh, Proceedings of London Math. Soc. vol. xi. No. 159. 
' Kirchhoff, Aih. der Konigl. Akad. zu Berlin, 1876 

' See Glazebrook, ' On the Keflexion and Refraction of Light,' Proc. Camh. Phil 
Soc. vol. iii. p. ,329. 

* See Ketteler, Voigt, etc. 
1885. o 



194 KEPORX— 1885. 

flexions. They have shown that, in general, plane polarised light becomes 
elliptically polarised by such reflexion, and have measured the difference 
in phase between the components polarised in and perpendicular to the 
plane of incidence and the ratio of the intensities of these two vibrations. 
MacCullagh ' was the first to attempt to express the laws of this 
elliptic polarisation mathematically. He supposes that in the case in 
question the angle of refraction becomes imaginary, so that we have 

sin 



, , sin / , . . \ 

in rf)':= Ll cos Y + i sm X ), 

m \ J 

J, cos 0/ / , ■ • /\ 

cos d)'= ;i( cosv' + ismx ). 



He then substitutes these expressions in the values given by Fresnel's 
theory for the amplitude of the reflected ray, which he shews may be 
written in the form a+fe v' — i. 

Thus the intensity of this ray will be represented by a^ + V', and the 
difference of phase between the incident and reflected rays will depend on 
tan ~^b/a ; a and b are functions of w, in', x, and x', and these quantities 
are connected by the equation sin'^^' + 008^^0' ^1, which leads to two con- 
ditions, giving m' and x' in terms of vi and x- 

The final formulae are : — 

(1) Light polarised in the plane of incidence. 

p = D' + cos'' - 2D cos <p cos (x-xO (4,q) 

D^ + cos'^ + 2D cos cos (x— x') 

t^n24=^^^^^^^pO. . . . (47) 
X COS'' (j)—D^ 

(2) Light polarised perpendicular to the plane of incidence. 

T/2 _ ''"'* cos'' + D^ — 2Dm^ cos cos (y + xQ fAQ\ 

7n* cos^ <p + D"^ + 2D»i2 cos f cos (x + x') 

tan2/- = -^P^\""^t'^"^^t^^^ . . (49) 

Where D'* = m'' + sin"* — 2m^ sin* f cos 2x 

and D'' sin 2 (x— x') = '"^^ ^™ ^X 



} • . (50) 



These formute are simplified in the case of metals from the considera- 
tion of the fact that the proportion of light reflected at normal incidence 
is nearly unity. It follows from this that m is very large and x' very 
small, so that we may put sin x' = 0, cos x' = 1 i^ ^^^c equations, and 
hence m' = cos /cos 0', 
And for Case I. — 

jj m' + m'"^ — 2mm' cos x ^ 

m"^ + m'"^ + 2invm' cos x 



, 2:rS 2inm' sin x 

\ m'^ — m^ ) 



(51) 



' MacCullagh, Pruc. Irish Acad. vol. i. pp. 2, 159 ; vol. ii. 376 ; Trans. Irish Acad. 
1 xxviii. Pt. I. 



ON OPTICAL THEORIES. 195 

and Case II. — 

j,2 1 + TO^W'* — 2«lMi.' COS X 

1 + m?rnl^ + 2min' cos v 

., o , • \ ■ ■ (52) 

, ct o' zmm sin v 
tan 2;r - = - ^ 

§ 2. Cauchy ' has also given equations founded on his principle of con- 
tinuity and the assumption of a peculiar form for the refracted ray which 
agree closely with those just established. His complete theory was never 
published by himself, and was first given by Eisenlohr. It has been 
further developed and criticised in some important points by Lord 
Bayleigh. Eisenlohr ^ takes for the displacement in a metal at a dis- 

— (p— ;•) 

tance r from a source of light the expression e ^' ' where X' is a com- 

plex quantity connected with A, the wave length in air, by the equation 

X = X' Re'«. 

Hence, using d and 8' to denote the angles of incidence and refraction, 
we have 

sin = Re'"^ sin 6' . . . . (53) 

The surface conditions of the continuity of the displacement and of 
the stresses become, as v^e have seen, identical with Cauchy's conditions 
of continuity of motion in the case in which the rigidity of the ether is 
the same in the two media, and the expressions for the intensity and 
change of phase for light polarised in the plane of incidence are most 
«asily obtained by transforming Fresnel's sine formula, which is strictly 
true. 

To effect the transformation put 



c» 


cos 


2u 


= 


1- 


cos 2a sin^ 


d\ 


C2 


sin 


2u 


___ 


sin 


2a sin2 d 





(93) 

m- a 

IP 
Then the intensity in the reflected wave is 

P = tan (/• - ^tt) .... (54) 
where 

cot/= cos (m + a) sin 2tan-ip— V 
while d, the change of phace, is given by 

tan d = sin (a + u) tan 2tan-i f^°lf\ ^ ^ (55) 

These values agree with those given by MacCullagh if we put 

R = m, a= - X, 

' Cauchy, C. B. t. ii. p. 427 ; t. yiii. pp. 553, 658 ; t. ix. p. 727 ; t. xxvi. p. 86. 
Ziouville's JomttmI, t. vii. p. 338. 

* Eisenlohr, Poffj. Ann. t. civ. p. 368. 

02 



196 EEPOET — 1885. 

and therefore c sec = m', u = x' \ C56> 

For Hglit polarised at right angles to the plane of incidence, Eisenlohr 
proceeds by transforming Fresnel's tangent formula in a similar manner, 

and finds , „ ^- 

I'2 = tan (g-i^) ' • • • (57) 

where 

cot g = cos (a — u) sin 2tan-' ( ^ J . . (58) 

and the change of phase is given by 

tan d' = sin (a — u) tan 2tan"'— — '■ — -, . . (59) 

^ ' K. cos 

Hence in the general case the ratio of the amplitudes of the two 
reflected components is tan /3 where 

cos 2/3 = cos (a + «) sin 2tan-M -^— — -^ J . . (60) 

and the difference of phase is given by 

tan (d' - d) = sin (a + u) tan 2tan-' ^_^_— ^ j . 



(61) 



These last equations depend on Fresnel's tangent formula, and this 
we know is not strictly true for transparent bodies. It is hardly 
probable, therefore, that the final equations for the difference of phase 
and the ratio of the amplitudes can be accepted as representing accurately 
the phenomena, and, in fact, Cauchy's theory as here developed isno great 
advance on MacCuUagh's original expressions, with which it agrees 
throughout. 

In this theory the expression for the disturbance in the metal 



IS e 



Ae -i ''^'""^ sin — (rR cos a - ct). 



k 



Hence the velocity of wave propagation is c/R cos a, as against c in 
air, and R cos a may be called the refractive index of the metal, while 
R sin a measures the co-efiicient of absorption. Now Jamin, Quincke, 
and others have measured the quantities d — d' and /3 of the formulas 
above, and from these Eisenlohr, in the paper already quoted, has calculated 
the values of R and o. He finds that for silver a = 83°. This result Lord 
Rayleigh has made the basis of a serious criticism on the whole theory. 

Lord Rayleigh ' endeavours to attach a physical meaning to the con- 
stants in these formula?, and in so doing starts from equations taken to 
represent the motion in the medium. 

Thus, for light polarised in the plane of incidence he assumes 

' dt^ dt Vdx* di/J 

' Hon. J. W. Strutt, ' On the Reflexion and Refraction of Light by intcnbel3r 
Opaque Matter,' PMl. Mag. May, 3 872. 



ON OPTICAL THEORIES. 197 

with the solutions for the two media, 



/ _- ^'g i(ax+b)j+vt) a. |^"e i(-ax+by+vl). 



(63) 

^ __ ^ g i{a,x+bij+vl)\ J ^ ' 

where 

a = — ^ cos 0, 6 =-— sin e, ^; = — — , 

\ A. A 

being the angle of incidence. If we put y^ = n/D, y^i = n/D,, we get 
from the differential equations — 

<±i;=.y'ri-i^)=,\s^j. . . (64) 
a2 ^ j2 ^^2 y^ D^^y 

From this we get sin 6' = - sin 9, and hence /x is the quantity which 

F 
we have denoted by Re'". 



Hence We'^^ = '^~Jl - i^). . . (65) 

yi^\ D^vJ 



Thus R2 cos 2a is positive, and R^ sin 2a is negative, so that 2a lies 
between and — ^tt and tan 2a = hlB^v. Again, in the expression for 
the refracted wave we have a^ = [ja when 6 is zero, and hence we find 
that the real part of /i is positive, the imaginary part negative, so that 
finally a lies between and — ^tt. This result is contradicted by Eisen- 
lohr's value for silver, in accordance with which a = 83°, from which it 
follows that the real part of /x^ is negative, and this Lord Rayleigh says 
is tantamount to assuming the medium to be unstable. Eisenlohr ' has 
repHed to this that the objection is really one to the form of equation 
assumed by Lord Rayleigh, and that according to other theories (e.ij. 
Helmholtz on anomalous dispersion 2) real negative values of /x^ are con- 
templated. With this reply we may in a sense agree. Loi'd Rayleigh'a 
objection is a valid one, however, against the supposition that the 
peculiar effects of metallic reflexion may be explained by the introduction 

of terms such as in the differential equations of an elastic solid 

ether, and forms an insuperable argument against the attempt to account 
for the effects on a purely elastic solid theory. When, however, we come 
to consider the theories depending on the mutual reaction of the ether 
and maiiter, we shall see that under certain circumstances the relation 
between the periods of the ether and matter molecules may be such as to 
give a negative value to fi^, and thus render possible Eisenlohr's value 
for a. 

The general value for a^ for any angle of incidence caay be shown to 
be given by 

«! = "^Rc < cos (u + a) + L sin (« + a) > . . (66) 

< ' Eisenlohr, ' On the Keflexion of Light from Metals,' Wi^d. Ann. t. i. 

2 See p. 220. 



198 EEPORT — 1885. 

c and ?( being defined by the equations of page 195, so that tbe expres- 
sion for the refracted wave is 

^^g?^p-Rcsm(« + a) sin— JRracos (u + a) + ysind + Yt\, 

where, it must be remembered, x is measured in the negative direction. 
Thus the coefficient of absorption is 

— Resin (u + a). 

According to the experiments of Jamin and Quincke, the refractive index: 
R cos a for metal varies between ^ and i. 

§ 3. Wernicke,' however, deduced, from some experiments of his own, 
values lying between 3 and 4. Wernicke's experiments, however, were 
made by measuring the light transmitted at various angles of incidence 
by thin films of metal, and assuming that the light absorbed by a thick- 
ness d may be expressed by fc/i''"^'^^', while the refractive index ft is given 
by sinf^/sinfl'. Eisenlohr, in the paper already quoted, shows that the 
quantity calculated by Wernicke is really {R^ + sin^y}^, and that his 
experiments confirm Jamin's and Quincke's. 

In the second paper quoted Wernicke suggests, as the complete equa- 
tions of motion, the form 



.+Zh^ = (A-B)f- + Bs^''^ + Zk't(v''-^) . . (67} 
dt'" \ Jdx dtf^y J 



and other equations might be suggested which would give for the dis- 
turbance in the metal due to a point source expressions of the form 



t.---_27r 



A£~^''sin 



fbr — vt\ 



Chapter VI. — Diffeaction and the Scatteking of Light by Small 

Particles. 

§ 1. The principle first enunciated by Huygens, and applied so trium- 
phantly by Fresnel to the phenomena of diffraction, which consists in 
breaking up a wave front into elementary portions, calculating the effect 
of each in disturbing a distant point, and then finding the total dis- 
turbance at that point by simply summing the effects due to each ele- 
ment of the wave front, is a direct consequence of the fact that the 
disturbances and velocities are so small that their squares and higher 
powers may be neglected. The differential equations found for the 
motion are linear, and the complete solution is the simple sum of all the 
individual solutions. Again, it is fairly clear that the disturbance pro- 
duced at any point by an element of a wave front will vary as the area of 
the element and the reciprocal of the distance between it and the point 
answered ; but it is not so clear how the effect is related to the angles 
which the line joining the element and the point make with the wave 
normal and the direction of vibration respectively. 

In Fresnel's theory of diffraction the consideration of effects produced 

• Wernicke, ' On the Keflexion of Light from Metals,' Pogg.Ann. t. clix. and clx. 



ON OPTICAL THEORIES. 



199 



by tlie vaxiation of these angles is omitted, and that, too, with perfect 
justice, for lie is only concerned with the effects in the neighbourhood of 
the normal to the primary wave, and the dimensions of the diffracting 
aperture ai'e small compared with the distance between it and the point 
at which the effects are considered, so that the change in either of these 
angles over the whole area of the diffracting area is small. 

Again, it is clear that the effect will be a circular function of r—vt, r 
being the distance between the element and the point at which the dis- 
turbance is sought, and v the velocity of propagation ; but the simple 
theory does not indicate the relation between the phase of this circular 
function and that of the function representing the disturbance in the 
original wave. 

§ 2. Both these questions received their complete and final answer in 
the year 1849 from Professor Stokes.' We will quote a few words from the 
introduction to his paper : ' TJ^e object of the first part of the following 
paper is to determine on purely dynamical principles the law of disturb- 
ance in a secondary wave, and that not merely in the neighbourhood of 
the normal to the primary wave, but in all directions. The occurrence of 
the reciprocal of the radius in the coefficient, the acceleration of a 
quarter of an undulation in the phase, and the absolute value of the 
coefficient in the neighbourhood of the normal will thus appear as parti- 
cular results of the general problem.' 

The equations assumed for the motion. are those of an elastic solid in 
the form given by Green — 



Jdx 



etc., where 



dx dy dz 



(68) 



In the preliminary analysis the important general theorem involved in 
the equations 

is proved. 

It is then shown that the solution may be written 

S = ?i 4- £2 



where 



and 



^ _ '^ = etc 
ay ax 

dx dy dz 

d^ _dj]2 
dy dx 

dx dy dz 

'Stokes, 'On the Dynamical Theory of Diffraction,' Trans. Camb. Phil. 
vol. ix. p. 1 ; Math, and Phys. Papers, vol. ii. p. 243. 



(70) 
(71) 



(72) 



Soc. 



200 



EEPOKT — 1885. 



and that hence 



^'="Mlr~^'°'^"^'^'^4l[, 



1- (yw'" - z^")dv 



(73) 



It is proved that ? and w', at", w'" satisfy the equation 

— . = a^ V ''t 

d iO 7 9 _, 9 



dt^ 



(74) 



. (75) 



and hence, hy Poisson's solution, 

where /and F are the initial values of I and dljdt respectively. 

If, then, the values of o and dljdt, w and dujjdt be given initially 
everywhere, the last equation, with the similar one for w, enable us to find 
S and w at any moment throughout the space considered, and then the 
equation (73) give us ^, ??, and C- 

In solving the equations for c, w, it is clear that if we first find the 
part of the solution due to the initial velocity, the part due to the initial 
displacement may be obtained by substituting in the solution for the 
initial velocity the initial displacement, and then differentiating with 
regard to the time ; and this proposition is proved generally for a system 
in which the forces depend only on the configuration of the system, and 
which is executing small vibrations about an equilibrium position. 

The integrals are then modified by suitable transformations. 



For 



L we have £,= -—, where ii'= 

dx 47r 



dv. 



Thus — 4<Tr\h is the potential of matter distributed throughout space 
with density S, and finally it is shown that 



^ = 



f 
47r 



(uqX + VqIj + Wqz) ~ (raf) 



. (76) 



where Uq, Vq, Wq ^^e the initial values of the velocities at the point x', y', z', 
at which dv is an element of volume, r the distance between x', y', z' 
and X, y, z, the point at which ^ is to be found. From this ^i can be found,- 



and in a similar manner So- The terms 



ir 



Vu 



<^[ arise from a wave of 



dilatation which is in general set up by any arbitrary displacement, and 
which travels through the medium with velocity a. If the initial disturb- 
ance be such that Cq = dcQJdt = everywhere, then this wave will not be 
formed. 



The terms 



''2) Vij 



^2 arise from a wave of distortion which ti'averses 



the medium with velocity h. If a disturbance be produced at a point O, 
and last there for a time r, then the motion at a point P, at a distance r 
from 0, will not commence until after an interval t, where t = r/a, P will 
be disturbed by a wave of dilatation lasting for an interval r ; it will be 
disturbed by the wave of distortion after a time rjh, and this disturbance 
will last for an interval t. 



ON OPTICAL THEORIES. 201 

The general integral is then applied to two cases, which must be care- 
fully distinguished from each other. In the first case, suppose that a 
periodic force acting parallel to a fixed direction acts throughout a given 
element of volume in the medium. Let the plane of xz contain the fixed 
direction, and let the axis of a; make an angle a with it. Let D be the 
density, and T the volume of the element, and let (DT)-\/'(Orf^ be the 
velocity communicated to it in time dt. 

Then 



r 

cos n ,( r \ . cos a fi^ 



47rD 

= 



sin a .f , r \ sin a f* 



^=4 



(77) 



Now, we have seen that in the ether the ratio ajb is probably very large, 
hence the first term in £, on which the normal vibrations depend, is pro- 
bably very small compared with the first term in C- The molecules of 
an incandescent body may be looked upon, at least very approximately, 
as centres of disturbing forces, and the above equations show us how it 
is that from such centres transverse vibrations only are propagated. 

If the ether be absolutely incompressible, so that a/b is infinite, then 
longitudinal vibration would be impossible. 

Suppose, now, the first term in 4 omitted, and pnt/(i) = c sin 27rit/X, 

Then for the most important term we have — 



y c sin a . 2 



"(fc^-r) . . . (78) 



and the first term in I is of the order Xjirr compared with the leading 
term in i^. Hence, except at distances from the source which are com- 
parable with the wave length, the terms in I may be neglected, and the 
motion is strictly transverse. 

This solution applies to the case of an element of volume vibrating in 
any given manner and emitting light into the surrounding space. Every- 
thing is symmetrical around the direction of vibration of the element of 
volume. It does not apply, as has been supposed by some writers, to 
the problem of diffraction ; for in this case we have a train of waves being 
propagated through an aperture, and producing disturbance in the medium 
beyond. 

Let us suppose the aperture to be plane, and that plane waves are 
bemg propagated through it in the direction of its normal; take 
this for the axis of x, the plane of the aperture being x = 0, and the 
axis of z the direction of vibration. Let Oj be a point in the aperture, 
and consider the disturbance propagated in a small interval of time r, 
across an element c^S, at Oi. This disturbance occupies a film of thick- 
ness It, and consists of a displacement f{ht') and a velocity hf'{ht'). 
Thus, for a point O, at a distance r from O^, and at a time t, given by 
i = t' + r/h, the initial disturbance is the above displacement and velocity 
extending over a volume brdS about ; and if I, m, n are the direction 



202 



REPORT 1885. 



cosines of Oi 0, measured from Oj, then the values of I, rj, Z depending on the 
initial velocity are — 

mnds 






(79) 



while the values depending on the initial displacement are- 

Pnds 



i" = - 



1," = - 



r = KI 



47rr 
Imnds 



ffit-A ' 



(80) 



From this it follows that the vibration at O, arising from that at 0,, 
lies in the plane through OiO and the axis of z, and is perpendicular to 
the radius OjO ; and if (j> be the angle between the axis of z and the line 
OiO, that between OiO and the wave normal, the value of this dis- 
placement is — 

' ^ . . (81) 



!: = ^ fl + cos o") sin ff fu-A 



Hence if 



f(bt) = c sin — bt, 



^ = f^/'l + cos e\ sin f cos — fbt-A . . (82) 

and the total efEecfc at will be found by integrating this over the whole 
wave front. 

We have thus found the complete expression for the law of disturb- 
ance in the secondary wave, and can see in what way it involves and (ji, 
and how its phase is related to that of the disturbance over the primary 



wave. 



The theory of diffraction given by Fresnel, and applied by him to 
points in the neighbourhood of the principal wave normal, is thus fully 
justified, since for such points 6 is small, and cos d therefore approxi- 
mately unity, while ^ is nearly constant. The expression shows that an 
addition of a quarter period must be made to the phase ; but this will not 
affect the form of the diffraction pattern obtained. 

But the results of the investigation are of even more importance in 
their bearing on the relation between the position of the plane of polari- 
sation and the direction of vibration of plane polarised light. For con- 
sider a ray diffracted in a direction making an angle d with the incident 
wave normal, and let the plane containing the incident and diffracted 
ray be called the plane of diffraction, and let the directions of vibration 



ON OPTICAL THEORIES. 203 

in the incident and diffracted rays make angles a,-, a,; with the normal to 
the plane of diffraction. Then the diffracted ray and the two directions 
of vibrations lie in the same plane, and the directions of vibrations are 
normal to the respective rays. Thus, if we form a spherical triangle by 
drawing lines from the centre of a sphere, pai-allel to the normal to the 
plane of diffraction and to the two directions of vibrations, since the 
direction of vibration in the diffracted wave is the projection on that 
wave of the direction of vibration in the incident wave, we have 

cos d = tan ftj cot a^ . . . . (83)' 

Now, let -cr and a be the azimuths of the planes of polarisation of the 
incident and diffracted Hght, measured from a plane normal to the plane 
of diffraction. Then, on Fresnel's assumption that the direction of vibra- 
tion is normal to the plane of polarisation, we have 

•=^ = 2 " "=2+""^' 

and tan a = sec 6 tan w ; 

while on MacCuUagh's hypothesis 

'B7 = a,, a = uj, 

and 

tan a = cos 6 tan to- ... . (84) 

These two formulae can be tested by experiment, and afford a means, 
therefore, of deciding between the two theories of reflexion, and of deter- 
mining the question whether reflexion be due to a change of density or 
to a change of rigidity in the ether ; for the values of a corresponding to a 
series of values of -ro- can be observed for any given angle of difiraction, 
and if the values of w be taken at equidistant intervals, the values of a, 
and therefore the positions of the plane of polarisation of the diffracted 
light, will not be equidistant, but will on the first hypothesis be crowded 
towards the plane of diffraction, while on the second they will be crowded 
away from that plane. 

Professor Stokes was the first to carry out a series of observations of 
this nature ; he employed a grating ruled on glass at the rate of 1,300 
lines to the inch, and the results of his experiments are decisive in favour 
of Fresnel's hypothesis. The experiments are troublesome, and the com- 
parison of the results with theory is complicated by the fact that the 
refraction through the glass plate on which the grating is ruled also 
produces a change in the position of the plane of polarisation. The 
amount of this change is the same on the two theories, and tends to- 
produce a crowding of the planes of polarisation away from the plane of 
diffraction, an effect opposite to that produced by diffraction on Fresnel's 
theory. Moreover, we may suppose that, when the ruled face of the grating^ 
is towards the incident light, either the diffraction takes place in air so 
that the wave enters the glass obliquely, or that the diffraction takes 
place in the glass after the light has entered the first surface normally, 
while when the ruled surface is away from the incident light the diffrac- 
tion may take place in air after passing normally through the glass, or in 
the glass so that the light after passing normally through the first sur- 
face emerges obliquely. 



'204 EEPOET — 1885. 

In any case we shall have 

tan a = m tan •ar , . . . . (85) 

where in is a function of the angle of diffraction and the refractive index, 
which can be calculated on either of the above hypotheses. 

The results were reduced by plotting from the experiments a curve 
with log m as ordinates and 0, the angle of diffraction, as abscissae. The 
curves given by the two theories on either of the above assumptions 
as to the relation between diffraction and refraction were also drawn, and 
a comparison of the two results ' leaves no reasonable doubt that the 
experiments are decisive in favour of Fresnel's hypothesis, if the theory be 
considered as well founded.' And, moreover, the comparison shows us 
that we must suppose the diffraction to take place before the refraction. 
Thus, when the grooved face is towards the incident light we must sup- 
pose the wave to be broken up in the air and then to be obliquely 
refracted through the glass, while when the grooved face is away from 
the light the wave must be treated as if it were diffracted in the glass 
and then obliquely refracted out, and Professor Stokes shows that it is 
a friori more probable from physical reasons that this is what takes 
place. 

§ 3. In the results of the experiments a certain amount of irregularity 
is pi'oduced by the want of symmetry of the grooves of the grating, and 
Holtzmann,' who in 1856 repeated Stokes's experiments, failed to obtain 
consistent results with glass gratings, and had recourse in consequence to 
a Schwerd's lamp-black grating ; with this he obtained results more in 
accordance with the theory of Neumann and MacCullagh than with that 
of Fresnel. 

Holtzmann thought that Stokes had neglected to consider the effect of 
the longitudinal waves, ' and to this neglect he attributes the error of 
Mr. Stokes ; ' and Eisenlohr,^ who * had not read the great paper of 
Prof. Stokes,' attributes to him the same neglect, and endeavours to 
give a theoretical account of the question from Cauchy's standpoint. 
Of course both these authors were quite wrong in their estimate of 
Stokes's work, and Lorenz ^ showed, from some decisive experiments of his 
own, that Holtzmann's results were due to an error of his method. Lorenz 
gave a fresh demonstration of Stokes's theorem, and arrived at the same 
results. Lorenz appears to consider his method as more general than 
that of Stokes, but this is due to a misconception on his part. The 
results of his experiments agree with Fresnel's theory. 

§ 4. The matter has since been experimentally investigated by 
Quincke,'* who showed that the method of forming the grooves on the 
grating was of the utmost importance, and whose experiments led to no 
decisive results, and moi"e recently by Frohlich.* Frohlich investigated 
the polarisation of the light reflected from a glass grating, but did not 
compare his results with theory. A few experiments of the same kind 
were made by Stokes in 1852, but he also omitted the comparison with 
theory. 

' Holtzmann, Pogg. An?i. t. xcix. p. 446. 

2 Eisenlohr, Pogg. Ann. t. civ. p. 3.S7. 

' L. Lorenz, Pogg. Ann. t. cxi. p. 315. 

■• Quincke, ' Experimentelle optische Untersuchungen,' Pogg. Anii. t. cxlix. p. 73. 

* Frohlich, Wiedemann, t. i. 



ON OPTICAL THEORIES. 205 

Rethy ' developed a theory whicli covers Frohlich's experiments, and 
arrived at a formula with which they agree closely, but his fundamental 
principles are at fault. 

In his solution Rethy adopts a method given by Kirchhoff to find the 
effects of a given source of light. 

The equations to be solved are, if we neglect the terms involving 
dilatation, 



etc., with the condition 
Take 



^^=v^vV 



du dv diu 
dx dy dz 



«& = ^- sm 27r I - - vj, + 2 I . . . (86) 



Then $ and its differential coeliicients satisfy the equations of motion,, 
and we require to find such solutions as will satisfy the equation of 
continuity. 

Rethy takes as solutions — 

da> 

• . (87) 



I. 

and 




d<t> d<t> 

'' = dy' ''=-dx' ^ = ^ • • 


II. 


u =- 


rf2<& d^^ d2$ tZ^d. 

~ dxdy' " —~ dydz' "^ — dx" '^ ly"^ 



. (88) 

The distance r, of course, is measured from a point on the grating to 
the point at which the motion is being considered. 

Now each of these expressions of course represents the solution due 
to some arbitrary motion set up somehow over the grating. In Case I. 
the motion is a periodic twist of each element about the axis of 2, while 
in Case II. it is an oscillation parallel to that axis. But Rethy does not 
show how this motion is to be set up, nor whether it can represent the 
effect of a train of plane waves falhng on the grating and there diffracted ; 
and a little consideration shows that it cannot, for, according to the 
ordinary assumed properties of the ether, we cannot get the wave of 
twist only without linear displacement ; the second solution corresponds 
to that due to the action of a periodic force at the origin generatino- a 
certain amount of momentum, and not to the complete effect of a train 
of waves. If we compare it with Stokes's solution, we see that it is that 
part which arises from the effects of the velocity propagated across the 
element, and omits the part due to the displacement. Stokes's solution 
applies to the case in which energy is being propagated by waves passing 
across the orifice into the medium beyond, and depends on the direction of 
motion of these main waves. Rethy's solutio4i is that which arises from 
a centre of vibration situated on the surface, kept in motion by some 
extei-nal force and sending out waves in all directions into the medium. 
Still, we can arrive at a formula of the same nature as that given by 
Rethy, and which does agree with Frohlich's experiments, by means of a 
simple extension of Stokes's principles. This consists in supposing that 

' ESthy, Wied. Ann. t. xi. p. 504. 



206 REPOBT — 1885. 

the incident waves set np vibrations over the surface parallel to a fixed 
direction, and that these vibrations lie in the same plane as the incident 
vibrations, while these vibrations set up others in the diifracted waves 
which lie in the same plane as those over the surface, and are everywhere 
normal to the diffracted rays. Then, if eo be the angle between the 
incident wave normal and the distui'bance over the surface, ^o a-^id the 
azimuths of the planes of polarisation on Fresnel's hypothesis measured 
from the plane of incidence in the incident and diffracted waves, and c 
the angle of diffraction, it can be shown that ' 

cos <po tan f = sin 2 cot Cq + cos S sin (po . . (89) 

This expression is given by Rethy, and agrees closely with the results 
of Frohlich's experiments which were made with two gratings — the one 
of 19' 76 lines to a millimetre, the other of 162 lines to a millimetre. 

The value of eo depends on the angle of incidence when this vanishes, 
so that the vibrations in the incident wave are parallel to the surface 
. Sq — 90°, and the above formula becomes identical with Stokes's. 

In comparing the two it must be remembered that the azimuths of 
the planes of polarisation are measured, in Stokes's expression, from the 
normal to the plane of incidence, while in Rethy 's they are measured 
from the plane of incidence. 

A careful series of experiments by Cornu'-^ also lead to the conclusion 
that the vibrations are normal to the plane of polarisation. This con- 
■ elusion coincides with that arrived at by Lord Rayleigh and Lorenz from 
considerations based on the phenomena of reflexion and refraction, and 
is further strengthened by the phenomena of polarisation produced when 
light is scattered by a series of small particles. 

§ 5. Before considering this, reference must be made to a paper by 
Professor Rowland,^ of Baltimore, on the subject. This paper will be 
more completely discussed when we come to the electro-magnetic theory, 
to which it more properly belongs. Professor Rowland, however, con- 
siders that he has discovered an error in Stokes's work, in that according 
to it ' when a wave is broken up at an orifice the rotation is left discon- 
tinuous by Stokes's solution.' It is not quite clear, however, how this 
criticism is intended to apply ; for the rotation in the main wave is 
-completely determined when the displacement is known. Now, Professor 
Stokes has shown that when the orifice is of finite size the aggi-egate 
disturbance at any point due to all the elements of the orifice, as found by 
his formula, is the same as if the wave had not been broken up. The 
rotation, therefore, as given by this formula is also the same. 

Again, the rotation is propagated according to the same laws as the 
transverse disturbance, and hence the elementary rotation due to a given 
element of a wave propagated in a given direction is related to the 
direction and to the total rotation of the element in the same way as the 
elementary displacement propagated in that direction is related to the 
Actual displacement. 

Thus, if the displacements over the wave be 

^ = 0, r, = 0, i: = c sin^^ {It-xX 

• See GlazebroQk, Proc. Camh. Phil. Soc. vol. v. p. 254. ' Cornu, C. R. 

' Rowland, ' On Spherical Waves of Light,' PMl. Ma^. June, 1884. 



the rotations are 



ON OPTICAL THEORIES. 20^ 



0, — c COS ^(bt—x), 0; 

A. A 



and the elementary rotation to which this gives rise is 

W2= — T-r <^^S (1 + ^°^ ^) s^^ 4' sin ^ (ht — r), 

A / A 

■>l> being the angle between the axis of y and the radius vector r. This 
elementary rotation takes place about a line perpendicular to the radius 
vector, and lying in a plane containing it and the axis of y. 

On passing from one medium to another the rotation is not neces- 
sarily continuous. The only surface conditions are that the displace- 
ments and the stresses are the same on the two sides of the surface of 
separation, and if the rigidity of the ether be diflPerent in the two media 
the rotations will be different also. But Professor Stokes's solution 
does not apply to this case, and for the case to which it does apply is 
complete. 

Chapter VII. — The ScATTERrao of Light by Small Particles. 

§ 1. In his experiments on the light scattered from precipitated clouds 
of fine matter, Tyndall ' showed that when the particles are sufficiently 
fine the light emitted laterally is blue in colour, and in a direction per- 
pendicular to that of the incident beam it is completely polarised. 

The full explanation of this was given by Lord Rayleigh in 1871 in a 

series of papers * having an important bearing on our present subject 

the relation between the plane of polarisation and the direction of vibration 
of plane polarised light. Professor Stokes, in his paper on fluorescence,^ 
had indicated the connection between the two questions. 

For consider a beam travelling horizontally, and look at it vertically 
downwards: the scattered light is in great part polarised in the plane of re- 
flection. If the scattering particles be small compared with the wave length 
of the incident light, the vibrations in an incident ray cannot be at right 
angles to those in a scattered ray. For the incident vibrations are 
affected by the dust particles, which in consequence of their very great 
mass relative to the ether remain practically at rest. 

We may treat the problem as if the dust particles moved exactly as 
the ether which they replace would do, and then superpose on this motion 
an equal and opposite motion. The first motion will not affect the 
regular propagation of the waves. In consequence of the second the 
particles become centres of disturbance, and set up other motions in the 
ether. These other motions will depend on the direction of apparent 
motion of the dust particles, and the optical effect in any direction will 
depend on the component of the motion at right angles to that direction. 
Now, the reflected ray is polarised in the plane of reflexion. If, then the 

> Tyndall, Phil. May. (4). vol. xxxvli. 

= J. W. Strutt, ' On the Light from the Sky, its Polarisation and Colour,' Phil 
Mag. Feb. and April, 1871 ; ' On the Scattering of Light by Small Particles,' June, 
1871. 

» Stokes ' On the Change of Refrangibility of Light,' Phil. Trans. 1852. 



208 EEPOKT — 1885. 

vibrations be in the plane of polarisation they will be at right angles to 
those in the incident light, while if the vibrations be at right angles to 
the plane of polarisation, they will come from the component of the 
original vibration, which is at right angles to that plane. If, then, on 
this supposition as to the relation between plane of polarisation and 
direction of vibration the incident light be polarised at right angles to the 
plane of reflection — i.e., in the case before ns in a horizontal plane — the 
light scattered in the vertical direction should vanish, and this is found 
to be the case. This general reasoning is substantiated by Lord Ray- 
leigh in the papers before us by mathematical reasoning, and, moreover, 
he shows that the intensity of scattered light in any direction varies 
inversely as the fourth power of the wave length. 

This may be seen from a consideration of the dimensions involved. 

The ratio of the two amplitudes in the scattered and incident vibra- 
tion will be a number. It must also involve the volume of the dust 
particles, being directly proportional to it, and it also will be inversely 
proportional to r, the distance from the disturbance ; it must therefore 
depend on T/X^r. 

The mathematical expression for the disturbance is found as follows: — 

Let D' be the density of the ether in the dust particles, D in the space 

surrounding them. Let the vibrations in the incident wave, when they 

o 
strike the dust, be given by A cos — hf. Then the acceleration is 



-^c^^ bycos^u. 



In order that the wave may pass on undisturbed through the parts where 
the density is D', force would require to be applied ; the amount of the 
force will be 

- AiD' - B) f ^y cos ^bt 

per unit volume, and hence a force 

A(B' -T>)(^y cos ^^bt, 

conceived to act at O, the position of the particle, gives the same disturb- 
ance as is caused by the particle. Now, we have seen in Professor 

Stokes's paper that a force F cos — bt per unit of volume produces a 

displacement at any other point given by 

y F sin a Stt ., , . 

which is this case comes to 

C = A — ^^ — -— ^ sin a cos -^{ht — r) . . . (90) 

where n is the angle between the radius vector r and the direction of the 
force F, and the displacement takes place in the plane passing through 
the directions of the force and the radius vector, and is at right angles to 
the latter. 



ON OPTICAL THEORIES. 209 

Lord Rayleigh's paper conclades with another proof of the formala 
which gives the motion due to a force acting parallel to the axis of z. 
Pat for the force Ze"", then the equations of motion become, when 
expressed in terms of the rotation, 



Hence 



dij ' 

(62v2+7i2)a,o = -f^| 
dz I 



]z|(^) ...... 



(91) 



47r6'^ 



2^ 
A 

and the integral extends over the space T, through which the force 



where h=^-='l 

A h' 



acts 



Within this space -^ri—-\ is sensibly constant ; and if w be the re. 

sultant rotation which will take place about an axis perpendicular to the 
plane through z and the radius vector, 



tl-TZ sin a e-'*'' 

w ==■ — . 



Hence ^= f c.cir= 'Lf smj« cos ^-(W-r) . . (92) 

J 47r6''r A 

In the second paper mentioned above Lord Rayleigh points out that 
the cause of reflexion may be diminished rigidity rather than increased 
density, and that in this case a scattered ray might be composed of 
vibrations perpendicular to those of the incident ray ; he then proceeds 
to_ describe experiments on the composition of the light of the sky, made 
with a view of showing that it is such as would result, according to the 
above formula, from light scattered by small particles. And in the third 
paper he discusses the motion in an elastic solid in which the density and 
rigidity vary from point to point. 

The problem is solved for two media differing slightly in density and 
rigidity, and it is shown that in a direction normal to the incident ray 
the rotation in the scattered ray, when the incident vibrations are parallel 
to z, is given by 

where 



J3 = 



Hence, if A« and aD are both finite, the scattered light can never 
vanish in a plane normal to the incident ray. 

1885. ^ P 



210 REPORT— 1885. 

Now we know from experiment that it does vanish, and hence either 
An or aD must be zero. If we put aD=0, it can be shown from the 
general expression for the rotation that there are six directions along 
•which the scattered ray vanishes, for the components of the rotation are 
given by — 

An yz 

^3 = - P — -'a- 
r r^ 

. . . . (94) 



'"l 


= 


p 


An 
n 


,.2 






= 


p 


An 


i- — . 


,.2 


Wj 


n 


,.2 





Now, there is nothing in the experimental results which at all leads to 
such a conclusion. If the hypothesis of a variable density be adopted, 
and A n be put zero, then, 

W3 = 

AD y 
'^'^l' D r\ (95) 

aD x\ 
^2=P -p, - 
-U r 

and the light vanishes in one direction only, viz. that of the axis of z. 
This result, of course, agrees with that of the former paper, and we must 
conclude that Fresnel's explanation of the cause of reflexion is the true 
one, while MacCullagh's is false, and that in plane polarised light the 
vibrations are perpendicular to, not parallel to, the plane of polarisation. 
The theory as left in this paper does not explain the phenomenon of the 
residual blue discovered also by Tyndall, who found that at a certain 
stage in the growth of the particle causing the scattering some light 
is discharged by the cloud parallel to the direction of vibration of the 
incident light, and that this Hght is of a very intense blue tint. 

Lord Rayleigh points out that this may be due to the higher powers 
of aD/D, which have been omitted, and in a more recent paper, based on 
the electro-magnetic theory, he develops this point more completely.' 

Chapter VIII. — General Conclusions. 

§ 1. Space compels us to conclude with this the general account of 
recent work on optical theories based solely on the elastic solid theory. 
Special problems of various kinds have received their solution, but to 
these we can only allude ; indeed, for several of them the general proper- 
ties of wave motion with the principle of interference are all that are 
required. Such, for example, are the papers by Prof. Stokes, ' On the 
Theory of certain Bands seen in the Spectrum,' ^ ' On the Formation of 
the Central Spot in Newton's Rings beyond the Critical Angle.' ^ — This is 
shown, as was suggested by Lloyd, to be due to the surface disturbance, 
which takes the place of the refracted wave when the angle of incidence 

> See p. 2.53. 

=" Stokes, Phil. Trans. 1848 ; 3Iath. and Phys. Pajiers, vol. ii. p. 14. 

» Stokes, Caml. Phil. Trans, vol. viii. ; Math, and Phys. Papers, vol. ii. p. 66. 



ON OPTICAL THEORIES. 211 

•exceeds the critical angle. — 'Oa the Perfect Blackness of the Central 
Spot in Newton's Rings, and on the Verification of Fresnel's Formulse for 
the Intensities of the Reflected and Refracted Rays.' ' In this paper is 
■given the now well-known proof of Arago's law that light is reflected in 
the same proportion at the first and second surfaces of a transparent plate. 
'On the Colours of Thick Plates,' ^ and ' On the Composition and Resolu- 
tion of Streams of Polarised Light from diSerent sources.' ^ 

In his ' Investigations in Optics, with special reference to the 
Spectroscope,' published in the ' Philosophical Magazine ' for 1879 and 
1880, Lord Rayleigh has considered the application of the principles of 
the wave theory to geometrical optics, and the construction of optical 
instruments. A full account of these is given in the article ' Optics,' in 
the ' Encyclopsedia Britannica.' 

Professor Stokes's great paper on Fluorescence '' is chiefly experi- 
mental. The cause of the phenomena is assigned to the vibrations set up 
by the incident light in the molecules of the fluorescent substance, which 
themselves react on the ether and emit the fluorescent light. According 
to Stokes the vibrations in this light are never of shorter period than 
those in the incident light; and he in a general way endeavours to 
account for this, and shows that if the force acting on a given matter 
molecule due to a given displacement be proportional to a positive inteoral 
power of the displacement other than the first, then the amplitude of°the 
displacements would involve the period, and there would be a tendency 
to increase the amplitudes of vibrations of lower period than that of the 
incident light, and to decrease the amplitudes in the case of vibrations 
■of higher period than that of the incident light. Thus, in a group of 
disturbed molecules we should expect all possible periods between two, 
the upper corresponding to the refrangibility of the incident light, the 
lower corresponding to the natural period of the molecules. This result, 
known as Stokes's law, has been the cause of much discussion. Some 
physicists 5 hold that they have found fluorescent substances which con- 
stitute an exception to it, while others," who have carefully repeated the 
•critical experiments, draw conclusions in accordance with the law ; and 
the weight of the evidence is with the latter. 

A general account of the principles of the elastic solid theory was 
given in his lectures at Baltimore last year by Sir William Thomson.^ 
To these we shall return in the next section. 

§ 2. In concluding this part of the report we may say, then, that 
while the elastic solid theory, taken strictly, fails to represent all the facts 
of experiment, we have learnt an immense amount by its development, 
and have been taught where to look for modifications and improvements. 
We may, I think, infer that the optical diff'erences of bodies depend 
mainly on differences in the density or effective density of the ether in 
those bodies, and not on diflPerences of rigidity. Fresnel's general theory 
•of the cause of reflexion is thus seen to be true, and Green's theory of 

' Camh. and, Buh. Math. Journal, vol. iv. ; ilatli. and Phys. Papers, vol. ii. p. 89. 
^ Camh. Phil. Trans, vol. ix. a Ihld. 

* Stokes, ' On the Change of Refrangibility of Light,' Phil. Trans. 
' Lommel, Pofjg. Ann. t. 143, p. 1.59 ; M'ied. Ann. t. iii. viii. x. ; Lubarsch, Wied. 
.Ann. t. xi. 

« Hagenbach, Poyrj. Ann. ; Lamansky, Journal de Phi/siqve, t. viii. ; Wial. Ann. 
t. viii. and xi. 

' Thomson, Lectures on Molecular Dynamics. 

P2 



212 EEPOiiT— 1885. 

reflexion and refraction can be made to agree with experiment by the 
simple supposition that for longitudinal and transverse disturbances 
respectively, the ether in a transparent body is loaded differently. This 
same theory of the loading- of the ether will not account for double 
refraction if we assume that the vibrations are strictly in the wave front. 
If, however, we admit that in a crystal the vibrations may be normal to 
the ray, instead of in the wave front, Fresnel's beautiful laws follow at 
once from the equations given by Lord Rayleigh, which are quite con- 
sistent with the theory of reflexion and refraction, but there is a diffi- 
culty in dealing with the pressural wave. Neither of the strict elastic 
solid theories of Green can be accepted as representing the flicts of ex- 
periment, and the interesting modification of Green's theory suggested by 
De St. Venant fails also. In all there are too many constants for the 
requirements of the experimental results, and the theories do not indicate 
the meaning of the arbitrary relations between these constants with 
sufficient clearness and certainty. 

The suggestions of Cauchy and Briot, with the elegant mathematics ot 
Sarrau on the periodic distribution of the ether in a transparent body, 
lead to es:pressions for the relation between the refractive index and wave 
length which agree well with experiment so long as we steer clear of 
substances which present the phenomena of anomalous dispersion, but 
of this they give no account. 

While the formulaj given by Cauchy and Eisenlohr seem to represent 
the laws of metallic reflexion witli considerable exactness, the theory on 
which these formulas rest, requiring as it does a negative value for the 
square of the refractive index, is inconsistent with the conditions of 
stability of an elastic solid. 

Nor is it surprising that a simple elastic solid theory should fail. 
The properties we have been considering depend on the presence of 
matter, and we have to deal with two systems of mutually interpenetrating 
particles. It is clearly a very rough approximation to suppose that the 
eSect of the matter is merely to alter the rigidity or the density of the 
ether. The motion of the ether will be disturbed by the presence of 
the matter ; motion may even be set up in the matter particles. The 
forces to which this gives rise may, so far as they afiect the ether, enter 
its equations in such a way as to be equivalent to a change in its density 
or rigidity, but they may, and probably will, in some cases do more than 
this. The matter motion will depend in great measure on the ratio 
which the period of the incident light bears to the free period of tbe 
matter particles. If this be nearlj- unity, most of the energy in the 
incident vibration will be absorbed in setting the matter into motion, and 
the solution will be modified accordingly. 

Part III. 

THEORIES BASED ON THE MUTUAL BE ACTION BETWEEN 
THE ETHER AND MATTER. 

Chapter I. — The Propagation of Waves through two mutually 
Interpenetrating Media. 

§ 1. In the optical theories hitherto considered attempts have been 
made to account for the phenomena of reflexion, refi-action, and dispersiott 
by the hypotheses of modifications produced in the properties of the ether 



O.N OPTICAL THEORIES. 213 

by the reaction of the material particles of the medium through which 
the light was being propagated. According to Fresnel the density of the 
ether is affected, while according to Neumann and MacCullagh it is to 
•changes in the rigidity that the effects are due. 

In both cases the direct effects of the communication of momentum 
from the ether to the material particles of the transparent medium is not 
considered. Fresnel, ' it is true, thought it ■ probable ' that the molecules 
of ponderable matter should partake of the movement of the ' ether 
which surrounds them on all sides,' and Cauchy,^ in one memoir, deals 
with the motion of two mutually interpenetrating systems of molecules, 
but without arriving at any specially important result. Voigt' states 
that about 1865 F. Neumann was in the habit of treating, in his lectures, 
the system of simultaneous equations relating to the motion of ether and 
matter. Briot,^ in his work on dispersion, considers the direct reaction 
between matter and ether particles, but in his final result equates, as we 
have seen,'^ the term expressing it to zero. 

§ 2. In 1867 a paper was presented to the French Academy by 
M. Boussine.sq ^ on the ' Theorie nouvelle des ondes Inmineuses.' In 
this paper the dynamical effects of momentum communicated by the 
ether to the molecules of ponderable matter are considered as the cause 
■of reflexion, refraction, polarisation, dispersion, &c. 

The ether is treated as homogeneous, and of the same density and 
rigidity in all bodies, and it is supposed that when light enters a trans- 
parent medium the molecules of that medium may be set in vibration 
isochronously with those of the ether. We have thus to consider the 
forces acting on such a medium, and these may be divided into three 
parts: (1) those which arise from the elastic reactions of the ether, 
(2) those arising from the elastic reactions of the matter, and (3) those 
arising from the mutual action between matter and ether. 

Now let us consider a small element of volume, containing both matter 
and ether. Let m be the density of the ether, /< of the matter, u, v, to the dis- 
placements of the ether in the element, U, V, W those of the matter. 
Then, using Green's notation, the force, measured parallel to the axis of x, 
arising from (1) will be per unit of volume — 

du dv dw 
where 6 = , ~ + , + -, . 

dx dij dz 

d-n 
For the forces arising under (2) we have to consider that in-jj^ acd 

d^V . . . 

fx -j^ ^ill be quantities of the same order ; but ju is very great indeed 

•compared with m, and hence U is very small compared with u. The 

' ' Premier !Memoire sur la double refraction,' OSuvres completes, t. ii. p. 278. 
^ Exercu'.cs d'Analjisc, t. i. p. 33. 
' Wied. Ann. t. xvii. p. 473. 

* Jissats sur la theorie mathcmatique de la luiuiire. Paris: 1865. 

* See p. 181. 

" C. R. t. Ixv. p. 235 ; Liouville's Journal, s. ii. t. xiii. p. 313. A most clear ac- 
count of this theory is given by M. de St. Venant in the article already quoted, 
'Theorie des ondes lumineuses,' Ann. de Chim. s. ix. t. xxv. p. 368 seq. 



214 EEPOKT — ]88o. 

forces (2) depend on U and its differential coefficients, and it is assumed 
in the theorj that in consequence of the excessive smallness of U they 
may be neglected. Again, let us suppose that the dimensions of the ele- 
ment of volume are large compared with the distance through which the 
action of an ether particle on a matter particle is appreciable. Then we 
may consider the mutual reaction between matter and ether as confined 
entirely to the element of volume considered, the actions taking place 
across the surfaces of the element will just balance each other, and hence,, 
if we consider the matter and ether as one system, the force (8) will be- 
zero, and the equations of motion will be 

J,. + M ^ = (A-B) ^_^ + B V he, etc. . . (1> 



m 



U is here the displacement of the matter occupying the same element of 
volume as the ether, whose displacement is u, but all the displacementa 
being very small, it is assumed that we may treat U and u as the dis- 
placements of the matter and ether, which when at rest occupy the same 
element of volume. Thus XJ, V, W are functions of w, v, w and their diffe- 
rential coefficients with respect to x, y, z, the initial co-ordinates, and may 
be expanded in terms of these, and it remains to find the form of the 
expansion. 

Conditions are, of course, imposed by the fact that the medium is 
isotropic, and it is shown that so far as second differential coefficients Me 
may write 

U = An + C ^^^ -I- D v^w, etc. . . . (2) 
On substituting this value of U, in the equation of motion, and assuming; 

Stt / m.r + tip + pz\ 

H = Me ' ^ V ~ "> ) etc., we obtain 

And these equations, of course, give a normal wave travelling with a 
velocity [ {X + 2^1 + 4(C + D) tt^, /r^} /(p + Ap,)]\ and a transverse 
wave with velocity [ {p -h4D7r2p,/r2} /(p -f- Ap,)]--. 

These velocities vary with the period of vibration in a manner which 
agrees, at least approximately, with experiment. It is clear that the 
coefficient A is positive, while the experimental fact that the velocity 
increases with the period shows that D is negative. The condition that 
A is positive merely implies that the ether tends to move the matter 
particles in the same direction as it moves in itself. 

If we suppose that the medium is not isotropically symmetrical, while 
at the same time it is such that the expi-essions retain the same form when 
two of the axes are turned through a small angle about the third, then 

terms B (-- — _-) come into the value for U, and these, it is shown^ 
\ dz ay J 

would cause the medium to produce rotation of the plane of polarisation 

of a plane polarised ray traversing it. This rotation would vary approxi- 

niately inversely as the square of the period, in accordance with the law 

discovered by Briot. By introducing higher differential coefficients into. 



ON OPTICAL THEORIES. 



215 



the value of U in terms of u, etc., it is shown that these approximate laws 
become, respectively, 



-=v„^(i + ^;+i;; + 



(4) 



V being the velocity, and Vq, £, etc. constants, while for \p, the rotation 
produced by a length z of the substance, he finds 



^=H 



1 + 



f f" 

o * 4 ' 



(5) 



For the explanation of double refraction Boussinesq supposes that the 
constants in the above formula giving U, V, W in terms of u, v, w may 
be functions of the direction of displacement ; but, arguing from the 
relative importance of A, C, and D in the ordinary theory of refraction 
(refraction is due to the existence of A, dispersion only to that of D), he 
supposes that we may to a first approximation treat C and D as constants, 
while we consider A as a function of the direction, and write for the 
three axes of symmetry, the existence of which is assumed, the values 
A(l + a), A(l + /3), and A(l + y). 
This leads to the equations — 



|i'=K(l + .)| + L(l + «)v'„ 



4!£ 
cPw 



K(l + 6)f- + L(l + h)^'v 
ax 

:K(1 + C) ~+U]. +C)V^W 

ax / 



(6). 



K, L, a, 6, c being functions of the other constants. It is clear that 
these are the same equations as were given by Lord Rayleigh,* and 
■which have been already considered. The wave surface they lead to 
is not Fresnel's, at least if we suppose the vibrations to be necessarily 
transversal. 

By retaining the terms involving the coefficient B, the elliptic polari- 
sation produced by quartz in directions oblique to the axis is explained. 
The formula for the difference in velocity in the two elliptically polarised 
waves traversing the crystal in any given direction agrees closely with 
that given by MacCullagh. In this case the squares of the velocities parallel 

to the axis are given by the expression N f 1 ± — r^ J , while the ve- 
locities in a direction making an angle with the axis depend on the 
equation 

w- = N + — pr — sm'' t) + — -— 

± |a/[(M - N)2 sin^ 9 +^-^ I 2N + (M - N) sin^ j 1 . (7) 



> See p. 179. 



216 



EEPORT — 1885. 



wbicli can also be expressed in terms of the principal velocities at right 
angles to the axis, for if w,, wj be the valnes of these, we have 



M + N = io,^ + u}'- 



(M - N)2 = (o 



2\2. 



') 






(w,2 + Wo") 



(8) 



The laws obtained in this paper are further developed in a second 
and third in the sanae joui'nal. In this third paper, Bonssinesq ' points 
out the necessity of including in the expression for U in terms of u 
diflFerential co-efficients of u, v, iv with respect to the time, and shows 
that the phenomena of magnetic rotation can be accounted for by putting 
in the case of a wave travelling parallel to z — 



U =Au 



dt 

V = A^- + 33 '~ 
dt 

W=: Aw 



(9) 



while the phenomena presented by refraction at the surface of a moving 
body are explained on the supposition that in finding d?\] jdP we have to 
take into account the visible motion of the body, and write 



d 



dt \ 



d , T d 

— + JU — - 
dt dx 



+ M f + 
ay 



o 



(10) 



L, M, N being the components of the velocity at the point x, y, z ; it 
is shown that in cases in which L, M, N are small compared with w', 
the apparent velocity of light in the body is 



o' = w + 



2 ' ' 



yu being the refractive index and V the velocity of the body in the 
direction in which the light is travelling. This, of course, is the formula 
given by Fresnel. 

§ 3. M. de St. Venant,^ in the article already quoted, sums up his criti- 
cism of the theory as follows : ' Les deux hypotheses principales de cette 
theorie nouvelle me semblent bien pres de s'elever a la hauteur de choses 
demontrees.' At the same time tbere remains the difficulty pointed 
out by Sarrau ^ of explaining on mechanical principles how the various 
terms in U, V, W arise, and on what physical phenomena the mechanical 
forces brought into action depend. 

§ 4. A further step in the progress of the theory was brought about 
by the discovery of anomalous dispersion by Christiansen ■* in 1870. Le 

' Bonssinesq, Liouville's Jounml, t. xiii. pp. 340, 425. 

- De St. Venant, ' Sur les diverses methodes de presenter la th6orie des ondes 
lumineuses,' Ann. de Chimie, t. xxii. 

' ' Theorie des ondes lumineuses,' Ann. de Chini. (4), t. xxvii. p. 272. 
* Fogg. Ann. t. 141, p. 479 ; t. 143, p. 250. 



ON OPTICAL THEORIES. 217 

Roux ' had found that vapour of iodine refracted red light more strongly 
than violet, and Christiansen, in the paper quoted, announced the result 
that for a solution of the aniline dye fachsin in alcohol the refractive 
index increases from the Fraunhofer line B to U, then sinks rapidly as 
far as G, and increases again beyond. The experimental investigation of 
the subject was continued by Kundt,^ who proved that this anomalous 
dispersion was marked in all substances showing strong surface color- 
ation, and that there was an intimate relation between it and the 
absorptive power of the substance. As the result of his experiments, 
Kundt was able to lay down the rule that in going up the spectrum, 
from red to violet, below an absorption band the deviation is abnormally 
increased by the absorption, while above the band the deviation is 
abnormally decreased. Kundt has been able to see this abnormal effect 
produced by the absorption of sodium light. 

On the old theory of dispersion, as developed by Cauchy and others, 
this effect was inexplicable. Boussinesq, it is true, had explained the 
phenomena in vapour of iodine by saying that it implied that the co- 
efficient D was positive ; and here, in a way, lay a germ of the truth, for 
the mutual reaction theory lends itself readily to a partial explanation of 
the whole. 

§ 5. Such an explanation was first given by Sellmeyer. He had 
been led to expect the effect from theoretical reasons in 1866,' and had 
endeavoured to discover it in a fuchsin solution, but without success. 
The action between the ether and matter is a periodic one of the same 
period as the light- wave traversing the ether. Owing to the enormous 
density of the matter compared with the ether its motion will in general 
be negligeably small ; but if it should happen that the period of the 
natural vibrations of the matter particles coincides with that of the 
incident disturbance this will no longer be the case. The energy of the 
light- vibration will be absorbed by the matter, and this absorption will 
tend to react on the light-disturbance, and will, it can be shown, increase 
the refractive power of the medium for disturbances of greater period 
than the critical one, and decrease it for disturbances of less period. 

The problem is much the same as that of a pendulum the point of 
.support of which is undergoing a small periodic disturbance. If the 
period of the disturbance be greater than that of the natural vibration of 
the pendulum the reaction of the pendulum on its support will tend to 
quicken the motion of the latter, and vice versa. 

Sellmeyer, in the papers referred to,^ published in 1872, after a most 
clear and able discussion of the difficulties of the elastic solid theories, 
adopts the hypothesis that the ponderable atoms vibrate, but with much 
smaller amplitudes than the ether particles. He then proceeds to consider 
the mechanism by which this is brought about. As with Boussinesq, the 
ether is supposed to have the same rigidity and density everywhere. The 
ether particles act directly on the matter particles, and in consequence of 
the vibrations of the former the equilibrium positions of the latter are 

' Ann. de Chiiii. S. III. t. xli. p. 285. 

= Poffff. Ami. t. 142, p. 163; t. 143. pp. 149, 259; t. 144, p. 128; t. 14.5, pp. 17 
and 164. 

^ Sellmeyer, Por/ff. Ann. t. 142, p. 272. 

■* SeUmeyer, ' Ueber die dxirch die ^5i;tlier-Schwingungen erreg^en Mitscliwingungen 
der Korpertheilchen und deren Kiickwirkung auf die erstern, besonders zur Erklarimg 
der Dispersion und ihrer Anomalien,' Poffg. Ann. t, 145, pp. 399, 520; t. 147, pp. 386, 
£25. 



218 BEPORT— 1885. 

disturbed and execute small harmonic vibrations ; but the matter par- 
ticles themselves vrill not generally coincide with their positions of 
instantaneous rest, and so we have to consider their vibrations about these 
positions. The equilibrium position of the matter at any instant is made 
to depend on the configuration of the ether at that instant, and may 
clearly be expressed, under the given circumstances, as a simple har- 
monic function of the time, so that if soi Vo (o be the equilibrium co- 
ordinates at time < of a given matter particle of mass m', we may put 

^u = «„ sin 27r ^ .... (liy 

r 

The ampUtude a^ will be very small. 

The force acting on the particle m' is then considered on the assump- 
tion that the action between two particles of ether and matter respectively 
depends solely on the distance, and may be expressed by mm'f(r), and it 
is shown that, supposing that/(r) is a continuous function of the co-ordi- 
nates,' the force per unit mass tending to draw in' to its instantaneous 
position of equilibrium is 

X=^%^-.^o) .... (12> 

where c is a quantity depending on /and the configuration of the medium, 
which may be a function of the direction. Thus, for an isotropic medium 
we have as the equation of motion of the matter particles — 



= - r^\^ -ftflSin ^ + ci) |, 



which leads, of course, to the integral 



i=-:^^aosm^(t+a) + hsm^l(t + ft) . . (13> 
t' — c r 

except when r^^, when 

t, = — TT - ttQ COS ^(r-La) -r 6sin ^ (t + l^) • • (14) 

t d d 

The question as to the legitimacy of the assumption involved in the 
equation 

tQ = ttg sin — {t + a) 

T 

is then discussed, and it is finally shown that it is correct. 

Again, it follows with great probability, from the experiments of 
Fizeau and Foucault ^ on interference with long difference of path, that in 
a ray of light the amplitude of vibration resolved in a given direction is not 
constant. We have, therefore, to treat a^ as varying — slowly, it is true,, 
compared with the rapidity of the vibrations — but still, it is probable, 
passing through many series of changes in one second. 

This leads to the result that h, the amplitude of the natural vibrationa 

' See Stokes, Srit. Assoc. ReiioH, 1862, p. 261. 
"^ Ann. de Chim. s iii. t. xxvi. p. 138. 



ON OPTICAL THEORIES. 219 

of the matter particle, will always be small unless r = c. Omitting, then, 
these from consideration, it follows that 

_2 

t' — c^ 

and the vibrations thus set up in the matter are shown to be the cause of 
refraction ; while if r = c we have 

^= —a cos 2:7 , 

da_. ^ . . . . (16). 

and these vibrations are the cause of absorption. 

So far, then, the results of this investigation agree with those 
Bonssinesq has given. They are, however, more general, in that they 
contemplate the possibility of the motions of the matter particles becoming 
appreciable, and so producing absorption. The next paper considers the 
question of the manner in which the action between the matter and ether 
aflects the velocity of light. At 6rst the direct efPect of the matter on the 
ether is neglected, and the refractive power of the substance is found by 
considering the energy lost by the ether and gained by the matter in each 
vibration. The refractive power is measured by n'^ — ], where w is the 
refractive index. 

Now consider a volume so small that all the ether particles in it 
may be treated as in the same phase, so large that it contains many 
matter particles, and suppose the reactions considered confined to the 
ether and matter of this element. 

Then it can be shown that if m' be the density of the ether, a' the ampli- 
tude of its vibration, the energy lost by the ether is (n^ — l)2x'^m'a'yT'^, 
while that gained by the matter is 2Tr'^ [Imr'^at)'^ J(t^ — c^)] jr^, whence the 
important formula 

r.2 



S-J/l-r -Mn^ 



„.-! = ^^!:i .... (17). 



is obtained. 

We may write this — 



,2_1 V 



1=Z 



r 1- <^«> 



where by E we mean that all the possible values of S, the free period of the 
matter particles, are to be taken into consideration. Now let us suppose 
that r is greater than c, and that the matter particles have only one free 
period, then the denominator of the fraction is positive, and decreases as 
r approaches c. The refractive power, therefore, increases as the period 
decreases (i.e., as we go up the spectrum), and as t approaches the critical 
value c (i.e., as we near the absorption band) the refractive power is 
abnormally increased. Above the absorption band, supposing there be 
but one, the fraction is negative, and decreases numerically in value as r 
is still further decreased ; and until r reaches a value for which l/r^ = 
l/o^ + K, n is imaginary. 



^^^ EEPOKT — 1885. 

As r decreases Still further the refractive power increases, but the 
refractive index is less than unity. 

The presence of a second absorption band above the first will of 
course, modify the conclusions. The change in refractive power is 
perhaps best illustrated by a curve, as is done in Sellmeyer's paper For 
the case above considered take values of the refractive power (n'-l) 
tor ord.nates and the reciprocals of the periods for abscissfB, then the 
equation in the case of one absorption band will be 



where a = i/c^ 

Thus the curve is an hyperbola, with the axis of .r and the line a; = a 
as asymptotes. If there be two absorption bands we have 

K , L 

y= — +i^. 

a—x b — X 

and in this case there would be two critical values for x (viz., a and h) for 
which the refractive power would become infinite, and near which the 
dispersion would be anomalous. 

In 1874 there appeared a paper by Ketteler i on the same subiect. 
the^fm^muir' ''^^^'" enunciated as the law of dispersion in a gas 



n^-} = ^ 



0' 



1 



I being the wave length and o, ft constants. 

I^urther comparison with experiments had led him to the formulaj 

l=Kr- + A+ — ~ 

and he now shows that by a proper interpretation of the constants this 
wilJ include the case of abnormal dispersion, 

§ 6. The theory of the mutual reaction between the matter and ether 
was next developed by Helmholtz, and his work was continued by 
Loramel, Ketteler, and Voigt. The method adopted by Ketteler differs 
somewhat from tiiose of the other three. Helmholtz ^ (in 1875), LommeP 
(m I87&), and Voigt -» (in 1883) start in the same manner to form the 
simultaneous equations satisfied by the displacements of the ether and 
matter particles in a given element of volume. Let n, v, w be the dis- 
placements of the ether particles of density ni in an element of volume cv, 
U, V, W those of the matter particles of density ^i. 

The forces on m are, as in Boussinesq's paper referred to above,-^' 
■considering only the components parallel to the ,«axis :— 

Ar,l, ^f^^}t^''^^^^lT'H^^^?''^^^^ aer sogenannten anomalen Dispersion,' Paw. 
^WM. Jubelband, p. 166. See also p. 181. 

\ Helmholtz, ' ZurTheorie der anomalen Dispersion,' Pog,/. A^m. t. 1.5i, p. 582. 

p 339 Theorie der normalen und anormalen Dispersion,' ^ned. Ann. iAii. 

* ^oi&t, Theorie des Lichtes fiir vollkommen durchsichtige Medien,' Mied. Ann. 
X, Aix. p, o7o. 

* See p. 213. 



ON OPTICAL THEORIES. 221 

(1) X', arising from external impressed forces ; 

(2) X, arising from the action of the other ether particles external to- 
the element cv ; 

(3) A, arising from the action of the matter. 
"While for fi, the matter particle, they are : — 

(1) S', arising from external impressed forces ; 

(2) ^, arising from the action of the matter external to the element ; 

(3) A, arising from the direct action of the ether. 

So that the equations of motion for an isotropic medium are — 

j^^ = X' + X +A. etc. 1 



m'—rir = -^ + A + A, 



dl^ 



etc. 



(19> 



a^' 



In all three theories the impressed forces are supposed to vanish, so that 
X' = S' = 0. The action between the matter and ether is supposed to 
be confined to the element of volume considered — i.e. the dimensions of the 
element are treated as large compared with the distance at which the 
direct action of an ether particle on a matter particle is sensible. 

This leads to the relation' J. + A = 0, independently of the value 

of^. 

The term X springs from the ordinary elastic reaction of the ether. 
Helmholtz and Lommel, considering only a wave of displacement in the 
direction of x travelling parallel to z, write for this term 

while Voigt considers the general forms of the expression given by the 
ordinary elastic solid theory, which, of course, reduces for the case of an 
isotropic medium to 

e V ^M + e' — , 
ax 

where 

5^ du , dv , dw 
= — + — \- — . 
fZ« dy dz 

For the forces represented by S, Voigt again considers the general 
case of a strained elastic solid, while Helmholtz and Lommel after him 
write 

>—l 9TT *> "' U 

Tor the proper values to be given to A and A there is great divergence 
of opinion shown in the three theories. 

' In his paper Lommel — as has been pointed out byJKetteler, ' Optische Contro- 
-^ersen,' Wied. Ann. t. xviii. p. 387, and "Voigt, ' Bemerkungen zu Herrn Lommel's 
Theorie des Lichtes,' Wied. Ann. t. xvii. p. 468— really employs the condition ^ - A = 0, 
for he estimates « and U in opposite directions. In his reply, Wied. Ann. t. xix. 
p. 908, Lnmmel endeavours to justify the signs used, but I think witliout success. The- 
effect will be to change the sign of a coefficieEt in one of the terms. 



222 REPORT — 1885. 

Helmholtz supposes, ' um die Bewegungsgleichungen zu vervoll- 
stjindigen,' that A is proportional to the relative displacement of the 
ether and atoms in the element of volume, and writes, therefore, 

A = /32(U- ?0- 

Lommel supposes that the action ' follows Newton's law of friction,' 
and depends on the relative velocity of the two ; he puts, therefore, 

A^fi'^CU-u). 
at 

The expression given by Voigt is much more complicated, and can 
iDest be considered later. Thus the equations we have to deal with are — 

(Helmholtz), and 






,|y=-,j>(n-„)-«'u-v'^;^ 



(20) 



ctr dz^ dt 



(I'll 9 a-U , -„)(l ,-r~r > 



(^2U ,.2''^TT ^ 2TT 2 ^?U* 



(21) 



(Lommel). 

The method of solution is the same in both, xi and U, which, strictly, 
are the displacements of ether and matter in the same volume in the dis- 
placed condition, are treated as if they were the displacements of ether 
and matter having the same undisturbed co-ordinates «;, if, z. This is 
legitimate, for U and n are both taken to be functions of the position of 
the wave front and the time only, and hence for all points on the same 
wave front U has at a given instant the same value. 

Assume, then, 

U = Ae-''-^ + '•'"-- '■"'■■tj • • • . (22) 

k is the coefficient of absorption, c the velocity, and 2!r /« the period of 
the vibration. 

On substituting these values in Helmholtz's equations, we find 

and 

2^ _ /3*y' 
en 



o^T;: (fiH^ _a^_ ^32)2 + ^4,,2 = ^ (say) • . (24) 



* In this equation tlie sign of 0- has been changed from that given by Lommel in 
accordance with the remark on p. 221 ; but see Lommel's reply to Voiot Wied -Inn 
t. six. p. 908. 

t A, of course, no longer has the same meaning as above, but is the amplitude of 
the matter vibrations. 



To solve these, pat 



ON OPTICAL THEORIES. 223 

] 

- = |0 COS (t», 

c 

h 

- = p sm (.). 

n 



Then 



1-^=p'cos2w=f' 



2^ 



= p^ sin 2w = G 



(25) 



Thus the value of Jc, on which the absorption depends, is proportional 
to y^, the coefficient of (T\J jdt in the equation, and vanishes if y^ is zero ; 
that is, if there be no frictional resistance to the matter motion. If h be 
•at all appreciable, the light-disturbance will penetrate but a little way 
into the medium, so that for transparent media we may treat h, and there- 
fore G, as small. 

In this case we have 

,2 = F+^j^ + ,etc., 

-while in the small term we may put for G/F the value 2A;c/w. 
In these circumstances, then, 



l=\..G-^'y' 



where 

^,2 = a2 + /32_yt/2^] 



(26) 



(27) 



Thus, as n changes kjc is a maximum when n = v; if the corresponding 
values of k and c be Lq and Co, then 

i-o I "^ 4^2(^2^ ^2) f-^ • . . (28) 

If the value of y be zero, then, for n = r, h is infinite compared with c ; all 
the light is absorbed. 

At the same time A is large, and we have, in dealing with the motion 
of the matter particles, to consider the limit of Ae-*o^. 

Turning, now, to the refraction, let C be the velocity of light in free 
space, N the refractive index, and suppose that the term ^G^/P may be 
neglected, then 

N2 = c^F = ^'" fl - — + /3^(-^ + 2^^-n^) -[ 

a2 L mn^ m^w2{(,.2_ ^2^)2 + 4^2(^2 + ^2^1 J • y-^y) 

and the maxima and minima values of this expression lead to the limiting 
values of the refractive index. 

These, it is shown, are given approximately by n^ — v'^=±l 2)'«t, which 



224 



REPOBT 1885. 



correspond nearly to the maxima of absorption. Thus, as we go up the 
spectrum, the refractive power is a maximum for the value oi n, given by 
7i,2 = ,/2 _ 2 r-nr, and a minimum for 7.^ = r^ + 2)"Z3-. There is, thei'efore, 
abnormal dispersion in the neighbourhood of the absorption band, but 
elsewhere the refractive index increases with n. Again, for large values 
of 11. we have N2 = C^to/o^. Now, if the density and the rigidity of the 
ether be the same in all bodies, we should have C^ = a^jm, and therefore in 
this case 1^ = 1. Thus the light of shortest wave lengths would be trans- 
mitted without refraction, contrary to experimental results. Sellmeyer, 
however, pointed out a method of explaining this difficulty which would 
be consistent with t"he supposition that C^ is equal to a^jm. According 
to him, we must suppose that there is a strong absorption band some- 
where just above the visible limits of the spectrum — that is to say, that 
the value of i^ — 2i"st is just beyond the limits of the visible spectrum, 
and that owing to this the refraction below the band is abnormally 
increased. 

The paper closes with a method for constructing the form of the 
refraction and absorption curves. 

Lommel's equations can be solved in a similar manner, and lead to 
similar formulfe. The two theories can best be compared with each 
other and with experiment by changing the notation slightly, and 
adopting that used by Ketteler ' in his criticism of the same. Let us put, 
therefore, 



a- =, 






(30) 



.-.<.. 5)) 



Then Helmholtz's equations (23) and (24) become 



( 



A-2 



m 






B^O-^^-n^) 



f.i,nn^{{ro'-n^y + 



nh'y^ 



K}. 



(31) 



and 



2k m 



B2,5K 



en a^ fimn ((j-q^ _ n^) + nh'^^K^} 



(32) 



and if we suppose X, X,, Xq to be the wave lengths corresponding to the 
periods n, I'l, and vq, we find 

B2 X;^ A\2_ _ ;^^~ 
BX2 , A"« X/VXo' J 






L 



f.tm X 



2 X2 



G = 



m 



jim X," 



"'(^-0- 



+ K2 






(33) 



' Ketteler, 'OiDtische Controversen,' Wied. Ann. t. xviii. p. 387. 



ON OPTICAL THEORIES. 225 



while the ratio of the amplitudes is given by 

B X2 



^=^' /^/./'V . -x.-, • ■ • m 



/{(^-O^-S) 



We can give a sort of physical meaning to the constants in these formulae 
as follows : A, is the wave length of the natural vibrations of the matter, 
freed from any action of the ether; Xq is their wave length on the suppo- 
sition that the action between the ether and matter is proportional to 
the displacement, while the ether remains fixed ; while I'l and j'q are the 
frequencies of these vibrations. B vanishes when there is no matter 
present, and since the expression shows that B/m is a number, it is 
probable that B will be proportional to the matter density ; while K is a 
number on which the strength of the frictional retardation depends. 

The quantity Xj, the wave length of the free vibrations (i.e. the dis- 
tance the light-wave travels in a natural free matter period) is immensely 
great compared with X, so that A is small compared with % except in the 
cases in which X does not differ greatly from Xq. 

It will be seen at once that the formula for F, on which, when the 
absorption is small, the refractive index depends, in terms of the wave 
length is very complicated. I am not aware that any attempts have 
been made to compare it carefully with theory. 

In the cases in which K is small (i.e., for transparent media) Xq will 
be an approximate lower limit to the wave length of the light trans- 
mitted. 

If we integrate the equation given by Lommel's hypothesis, modified 
so as to agree with the principle of action and reaction, we find 



F*=^ 

«2 






• (35) 



where B' is a constant related to the /3- of Lommel's equations in the 
same manner as B is to jp above. If, however, we take Lommel's ex- 
pression strictly, to which he still adheres,' the sign of the fractional 
expression must be changed. 

If we retain the negative sign the formula (35) fails to represent the 
facts. Neglecting for a moment the effect of absorption, and supposing the 
ether to be of the same rigidity and density as in free space, the square of 
the refractive index will be rather less than unity for the longest waves ; it 
■will then decrease to a minimum value, which will be positive, and then 
rise rapidly through the absorption band, for which X = Xq, reaching a 
maximum a little above the band, from which it will again fall. Absorp- 
tion efifects will only slightly modify these conclusions. Thus the 
spectrum above the band ought to be more refracted than that below, and 
except just near the band the refractive index should decrease as the 
wave length decreases. This is fatal to the theory in this form. In its 

* This becomes the expression given by Lommel on substituting B'/m — K = €=, 
^i" \. B' =wi(K — €), and interchanging m and /x. 

' Lommel, ' Zur Theorie des Lichtes,' M'ied. Ann. t. xix. p. 908. 
1885. Q 



226 KEPOBT— 1885. 

original form it is not open to this criticism, and accounts for the facts, 
bat its fundamental equations are hopelessly at variance with Newton's 
third law, so long, at least, as we suppose the mutual reaction limited to 
that between the matter and ether in the element of volume considered 
— that is, so long as we may suppose that there are many molecules in an 
element of volume. The original formula for dispersion leads to results 
which, as Lommel ' has shown, agree fairly with experiment ; and by carry- 
ing the approximation a step further the agreement becomes closer still, 
so that his fundamental equations might be taken as an empirical repre- 
sentation of the facts with some approach to the truth. 

Voigt's theory differs from these mainly in the values assigned to A 
and A and the methods by which those values are obtained ; and before 
treating at length of it, it will conduce to clearness if we consider 
Ketteler's theory, the results of which have considerable resemblance to 
the two already mentioned, while the work itself is earlier than Voigt's. 

§ 7. Ketteler ^ is the author of a large number of papers on this 
subject, and the form in which he has presented his theory has varied 
somewhat, though the central idea which he has endeavoured to express 
has remained the same throughout. The idea seems to be as follows. 
The exact expression of the action between matter and ether, the A and A 
of the fundamental equations, is unknown to us, and we must therefore 
endeavour to eliminate it from the equations. This we can effect by con- 
sidering the work done per unit time on the whole system, into which, of 
course, the mutual reactions will not come, and equating it to the rate of 
change of the kinetic energy. This alone, of course, will only lead to one 
equation, and though in some of his work Ketteler appears to obtain two 
out of it, this, as we shall see shortly, is done by the aid of an additional 
hypothesis. 

It is, however, not till some of the later papers that these views are 
completely developed. In his first paper ^ he assumes that the action of 
the matter on the ether is to increase its rigidity by the quantity ea, and 
to introduce a resistance acp, where £ is constant for the medium and a is 
some unknown function of its dynamical condition, while the forces on the 
matter are a(£' v^p' + kV')> f' being the matter displacement, so that, 
considering the motion parallel to x, we have for the ether 

and for the matter \- . ■ . (36) 

Arguments similar to those employed by Sellmeyer lead to the equation 

N2-l = ^ (37) 

and on multiplying the first of the equations of motion by p, the second 

' Lommel, ' Ueber das Dispersionsgesetz,' Wied. An?i, t. xiii. p. 353. 

^ Since the above was sent to press, Ketteler has published his optical theories in 
the form of a book, Theoretische Optik : Braunschweig, F. Vieweg und Sahn, 1885. The 
fundamental equations are formed as indicated below (Equation 43), and the remarks 
made in connection with that section apply. 

' Ketteler, 'Versuch einer Theorie der (anomalen) Dispersion des Lichtes in 
einfach- und doppelt-brechenden Medien,' Carl Repertoriwrn, t. xii. p. 322. 



»» ^7r= (« + «°) -A + "^P 



ON OPTICAL THEORIES. 227 

by p\ we find that the condition (37) reqaires the coeflacient of a to 
vanish separately, and we are led to the two equations 






(38) 



and these are the two fundamental equations of the theory, from which an 
expression is found for the refractive index in terms of the wave leno-ths 
and constants, viz. : — ° 

N2 = N»^ +^v^ (39) 

— -1 
\' 

wrhere the S must be taken to include the different kinds of matter 
|)articles m the medium. So far, at any rate, the theoretical bases ot 
these expressions are no more secure than those of Lommel and Helm- 
holtz. Ihe dispersion equation, however, is much more simple than that 
given by Helmholtz, and agrees well, as Kefcteler i has himself shown with 
experiment. 

A second paper 2 develops some further consequences and traces the 
torm ot the dispersion curve in various circumstances. 

In a third paper ^ the principles of the theory are stated and applied 
to doubly refracting media, but the equations from which he starts- the 
same as those given above, only written with three co-ordinates— do not 
express the physical facts which they are intended to do, and the theorv 
deduced can only be considered as empirical. 

A further attempt, based on this principle of energy alone, is made in 
a more recent paper ' to establish two independent equations Thus the 
ether mass in an element being displaced a distance ds, the matter mass 
•as ; then the equation 



'»i?*+-'s^*' = «S* . . . (40) 



IS supposed to express the law of the conservation of energy for the ether 
motion ; it neglects entirely the forces on m' from the action of neiffh- 
ftouring matter. The conservation of energy principle alone will ^ive 
but one equation when applied to the system, though it will of course 
eliminate the unknown reactions between matter and ether 
w,-fl T^^'^ remarks must be made with regard to other papers ^"^ dealing 
with the formation of the fundamental equations. The equations D of 
tne last article referred to are only true on the assumption that the 

' See p. 181. 
Ann^^lioTv-'m^ Zusammenhang zwischen Absorption und Dispersion,' P^^^. 

breclSn Mit'tpl'n ''2''°"^/''i?''?'''^°^ und Absorption des Lichtes in doppelt- 
orecnenaen Mitteln, Pogfi. Ann. Erganzung, Band viii. p. 444. 

5 -^^f 1 .'Su' I^^spersionsgesetz,' Wied. Ann. t. vii. p. 658. 
AMd £r mJ ..?^n ^r ^^^o^'^^^iiden Anisotropen-Mittel,' Mo7iatsier. der Koniql. 
t S n 387 -KrwS '"' ^°^.i^' ^^ 'Optische Controversen,' Wied. Ann. 
X. xviu. p. 387 , Erwiederung auf Herrn Voigt's Kritik,' Wled. Ann. Bd. xxi. p. 178 

Q2 



228 BEPOET — 1885. 

reaction of the matter on the ether produces a force —m'C — ^* while 

the action of the ether on the matter is expressed by a force — m C — ^• 

and, indeed, in his most recent work on the subject ' he realises clearly 
that the energy principle only leads him to one equation, viz. : — 

m -^dp + m' — ^- dp' = e\7^pdp — icp'dp' . . (41) 

e being the rigidity of the ether in free space — and then combines with 
this a ' second equation relating to the special mode of action of the 
matter particles, which can be no other than the renowned fundamental 
equation of Bessel's theory of the pendulum ' ; this may be written 

It is then further assumed that the matter particles exert a force /jm'p' 
on the ether, and the equations finally become — 



»i§-m'Co^'=evV+A»y 



111 



'c f^V , ,„/ dy _ /,,„/ : ., <ip' 



C 



dt 



. ,dy ( , . dp'\ 



(43) 



leading to the equation 



N^-Ki = 



N^^- No'+V-l(Nl -l)K^' 



~\ 



,^-iw-ikA 



(44) 



■where K is a quantity depending on y. When K is small, as is always 
the case in transijai-ent media, this becomes the formula already men- 
tioned, which has been tested over so wide a range by Ketteler. It is 
clear from these last equations that the action of the matter on the ether 

is represented by ?)i'Co'-ri- + P^i'p', and of the ether on the matter by 

in ^ T^ jg (Jifficult to conceive of the mechanical principles which 
° df^' 
would lead to these terms as they stand, and the occurrence of the 
imao^inary quantity in the expression for the refractive index, to which 
they lead, is a blot on the theory. 

§ 8. In fact, the form of the equations given in his earlier papers ^' 
leads to results which are more directly intelligible, while the equations 
themselves can, it seems to me, be established by the aid of a suggestion 
due to Ketteler himself (' Eine dritte Annahme,' p. 397). 

For, taking the notation employed when considering Helmholtz and 

* In Ketteler's paper ^, |' are used for the displacements. I have retained p, p', in 
accordance with the notation ah-eady employed. 

' ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199. See also 
Ketteler, TheoretiscJie Ojdilt, p. 85, et seq. 

' Ketteler, ' Optische Controversen,' Wied. Ann. t. xviii. p. 387. 



ON OPTICAL THEORIES. 



229 



Lommel, let us assume, according to this third supposition of Ketteler's, 
that the reaction between the ether and matter is proportional to the 
relative accelerations of the two. Helmholtz supposes it proportional to 
the relative displacements, Lommel to the relative velocities. In this 
<jase, then, 



and hence 



A=-/3^J^(.-U), 



m5^+/32^^(t,_U)=.N, 






<P 



Thus 



7)1 



iVy, _ fihn d^XJ _ mX 



■n 



7W. + /32 dt^ m + /32 

2 ,lfi ^ /- ,7/2 — .. _ ,'2 



df' 



dt^ 



P-P' 



(45) 
(46) 



And, with Ketteler's assumptions as to the forces X and ^, these may be 
written as follows — 



d-n „, 



d<2 



.(Pu 
dz^ 






(....f)j 



(47) 



which are the same in form as Ketteler's equations, though a^ is not the 
rigidity of the free ether, while there is a relation between C and C, for 



and 



C'=-'^. 



c = 



fi m + jy^ 
ft' 



(48) 



However, this does not matter, for it is the product CC which comes 
into the fundamental equations of the solution, and we find 

2 



1 7-2 in 



L. °(^-0 



( 






1)%K^^^ 



A,^ 



2k VI y 

en 



DK?- 






K2 



^2 



(49) 



(50) 



where D = CC, and K is proportional to y^. 

The quantity a^/m is no longer the square of the velocity in free 
space, and cannot be put equal to unity, and, in fact, a'^/vi will be the 
square of the refractive index for very long waves. Ketteler (p. 398) 



230 EEPORT— 1885. 

seems to consider it an objection to Lis theory that it gives a value dif- 
fering from unity to the refractive index for infinite waves, but the objec- 
tion is not, I think, serious. As has been stated before, the dispersion 
equation given by his theory has been repeatedly tested by Ketteler,' 
and the agreement between theory and experiment is very satisfactory. . 
Thus we may probably look upon this equation as one established em- 
pirically by his experiments, and while not agreeing with the reasoning- 
employed by Ketteler in forming his equations of motion, may see in 
those equations the expression of a possible law of action between matter- 
and the ether. 

§ 9. Let us now turn to Voigt's work, which is of more recent date. 
He has been a severe critic of his predecessors, and objects strongly to 
various points in their work. 

In his first paper ^ on the subject Voigt, following Boussinesq,^ 
remarks that mtVuliW and /jid^U Idi^ being quantities of the same order, 
U will be very small compared with u because fi is very large compared 
with m ; it is therefore not necessary to introduce terms involving U 
into the diiFerential equations for u. To this we may reply, (1) that it is 
quite possible that the coefficients of U and its differential coefficients- 
involve fi the matter density, and that in consequence the terms in ques- 
tion are comparable with md^itjdt^, and (2) that in the critical case 
near the absorption band the value of U becomes large, and may be 
quite comparable with ii. 

Voigt also objects to the form adopted for S in all the previous 
theories, viz. — (kU + ydV jdt), pointing out that Helmholtz introduced 
the kU ' zur Vereinfachung der Rechnung,' and the ydV/dt to explain 
the transformation of light-energy into heat. If the ponderable matter 
is to be looked on as an elastic solid, then, according to Voigt, we ought 
to put for S terms like cr \7 ^U + b^dS f dx. To this Lommel replies*' 
that the matter molecules each as a whole are not affected by the pas- 
sage of the wave of light, but that intra-molecular or atomic motions are 
set up, and that the forces arising from these are represented by his 
terms, how he does not explain. 

Of course, since it is assumed that U = Ae'-'^*'"^''"'^'",. 
V^U= — {h + iy;/c)-U, the difference between the two will only show 
itself in a change in the refraction formula. 

The main criticism * of Ketteler's work relates to the method in which 
the equations are obtained. To this we have already referred. 

§ 10. After these criticisms we turn to the consideration of Voigt's ^ 
own theory. His fundamental equations are, as we have seen, 

' Ketteler, ' Constructionen zur anomalen Dispersion,' ^]'ied. ^1««. t. xi. p. 210; 
' Einige Anwendungeii des Dispersionsgesetzes auf duichsichtige, halbdurchsichtige 
und undurcbsichtige Mittel,' Wied. Ann. t. xii. p. 363 ; ' Experimentale Untersuchung 
iiber den Zusammenhang zwischen Refraction und Absorption des Lichtes,' Wied. 
Ann. t. xii. p. 481 ; ' Photometrisclie Untersuchungen,' Wied. Ami. t. xv. p. 336. 

" ' Bemeikungen zu Herrn Lommel's Theorie des Lichtes,' Wied. ^M7i. t. xvii.p. 468. 

» Seep. 213. 

* Lommel, ' Zur Theorie des Lichtes,' Wied. Ann. t. xix. p. 908. 

^ Voigt, ' Ueber die Grundgleichungen der optischen Theorie des Herrn E. 
Ketteler,' Wied. An7i. t. xix. p. 691 ; ' Duplik gegen Herrn Ketteler,' Wied. Ann. t. xxi. 
p. 534; Ketteler, ' Erwiederung auf Herrn Voigt's Kjitik,' Wied. Aim. t xxi. p. 178;: 
' Duplik gegen Herrn Voigt,' Wied. Ann. t. xxii. p. 217. 

" Voigt, ' Tlieorie des Lichtes fiir vollkommen durchsichtige Median,' Wied. Ann.. 
t. xix. 13. 873. 



ON OPTICAL THEORIES. 



231 






■ (51) 



X' and S' are each put equal to zero, and the condition A + A = is 
assumed ; that is, it is supposed, as we have stated before, that the sphere 
of action of each ether particle on the matter is small compared with the 
dimensions of the element of volume considered. 

An expression is then found for the rate at which work is being done 
on the compound medium, and the condition formed that this expression 
should be a function of the time only. 

So far as the terms depending on the mutual reactions are concerned, 
the rate of increase of the energy is given by 



s;=.p(™..)„(A'?(^.B.!0:^).c*^))- 

+ S j d (surface) Afc 8/,^,. = J (vol.) + J (surface) 



(52) 



where the S implies that more than one medium may come into con- 
sideration, and the integrals are to extend over the whole volume of each 
separate medium and all the interfaces between the media, these being 
indicated by J (vol.) and J (surf.) respectively. 

Forms are then found for A, B, C which make J (vol.) a complete 
differential coefl&cient with respect to the time, and at the same time lead 
to linear equations of motion which admit of solution in the form 
u = '^Ae^'-' *'""'*' "~ * '''\ Four possible forms are found, which are given 
below. 

(1) - A, = «i(it - U) + 03(1' - V) + 0^(10 - W) 

/ox A d(v-Y) d(w - W) 

(2) A,=p, ^ ^^^ ^ -p, ^,^ 



dt 



(3) -A, = r, 



d2(«_U) , d-^iv-Y) d^(iv-W) h ■ (^3) 



dt^ 



+ s 



df 



+ S2 



dt^ 



(4) 



_ d^(v-Y) d^w-W) 



23 



dt^ 



df^ 



It will be noticed that (1) gives us Helmholtz's theory ; (3) gives 
us Ketteler's in the modified form I have suggested ; for an isotropic 
medium it is shown that the coefficients and s vanish. Lommel's form is 
not included in the above ; it is therefore, we see, inconsistent with the 
conservation of energy in the medium. 

But there are other terms in the volume integral J (vol.) which will, 
when combined with suitable terms in the surface integral J (surf.), make 
the whole up to a differential coefficient of the time. 

These terms are given by 



-A = 



dK 
dx 



dij 



dA, 
dz 



(54) 



232 EEPOET— 1885. 

etc., and lead to terms in the volume integral 

d (volOrA.. -^^(J-^) + A„ i^X!i^) + A. ^^!(!i^U) + . . 1 
L dtdx " dtdu ' dtdz ^ • • • I 

■= -^ (let us suppose) . (55) 

Then /' is a function of ^^"~ , etc., and four possible forms are found 

for A^, etc., viz. putting x, etc., for the difiPerential coefficients 
dJu-V)^ etc. 
dx 

(5) /'j, a homogeneous function of xi . . . X9 

-(A,).5 = 'p',etc. 

Thus — A,, = Em, ,. x , etc., 
with n^=n^;. 

(6) -A. = 2^.,% etc., 

dt 

with the conditions p,-, = 0, 

giving /g = constant. 

(7) -A -Sr ^*X.- 

with ?-,j = »v,, 

(8) -A, = ^,,^. 

with2,.i=0, qu=-qj;, 
and -/' = SSg,/^- ^'_^ixA 

We have thus eight possible forms of values for A, etc., all or any of 
which may occur in the equations. In the equations for the ether, 
U, V, W, being very small compared with ii, v, w, are omitted. 

An isotropic body is one in which no one direction differs in its 
properties from any other. For such a body it is supposed that the forces 
defined by 2, 4, 6, and 8 above do not exist, and a, a' being the 
coefficients in -2/'^ and - 2/'^ respectively, it is shown that the equation 
for plane waves travelling parallel to z is — 



ON OPTICAL THEORIES. 233 

and hence, 



1 


m{e 


> + «) 
e 


4aV2 

\2 


s^ 


m 


+ r- 


n\^m 



4eir2 

X being the wave length in air and N the refractive index. 
The complete valne for A is — 

.._/i(^J2,..n^),.*ii=n)_.0.-^) .(57) 

and in the above equation (56) U has been treated as small compared 
■with u. 

We see that the first and last terms are those given by the theories 
of Ketteler and Helmholtz respectively ; Voigt's more general theory 
includes them as particular cases. The first and third terms occur in the 
theory developed by Boussinesq, which is also included in Voigt's. 

In a further paper, in reply to some ci-iticismsof Lommel, who argues 
that a wave propagated through the molecules of the medium must be a 
BOund-wave, and that therefore the matter motion which affects the trans- 
mission of light must be i'7?ira-molecular not «(<er-molecular, Voigt 
shows,' by taking the matter motion into account, that the velocity of wave 
propagation in a medium constituted as supposed will be given by a 
quadratic equation. One root of this quadratic will be comparable with 
the velocity of light in this medium, the other with that of sound ; while 
the ratio of the energy of the matter to that of the ether in the light- 
motion is the reciprocal of the same ratio in the sound-motion. 

Voigt's theory applies only to perfectly transparent media, and its aim is 
to show that the optical properties of all such media can be explained on 
an elastic solid theory by considering the mutual reactions of two 
mutually interpenetrating elastic media. The author does not touch the 
problem of absorption, because for that purpose we require to deal with 
the molecular motion to which, in his opinion, heat effects are due, and 
these lie outside the domain of elastic solid theories. He does, however, 
deal with double refraction, circular and elliptic polarisation, and the 
various problems connected with reflexion and refraction. Most of these 
have been treated of also by Lommel and Ketteler. 



Chapter II. — Double Refeaction. 

We will consider first the problem of double refraction. All three 
explain it in a similar manner. Within a crystal the action of the 
matter particles on the ether will depend on the direction of vibration, 
and some or other of the constants of the theory will be functions of this 
direction. It is assumed that the ether remains isotropic, and that there 
are three axes of symmetry, which are taken as those of the co-ordinates. 

§ 1. Lommel 2 in his theory treats the constant we have denoted by 
a^ as a function of the direction, ft'^, which determines the action 
between ether and matter, and y^, on which the frictional effects depend, 

' Voigt, ' Zur Theorie des LicMes,' Wied. Ann. t. xx. p. 144. 

* Lommel, ' Theorie der Doppelbrechung,' Wied. Ann. t. iv. p. 55. 



234 REPORT— 1885. 

are left invariable, so that the ether equations remain unaltered, and the 
matter equations become — 

and similar equations with a^ and a-^. It has been shown by him that 
for a transparent medium the velocity is given by 1/r, where r is a 
radius, drawn in the direction of displacement of the surface — - 

(^^ + 2/^ +^^ - 1) ( ^ti + N;ti + NT^i) =«=^ + 2/^ + ^^ (59) 

and the directions of vibration are the axes of a section of this surface by 
the wave. 

These results are at variance with experiment, which requires that the 
wave surface should be that of Fresnel, and no reason is assigned in 
the paper for making a? rather than /3^ or y^ a function of the direction. 

Circular polarisation and the rotation of the plane of polarisation ' 
are also treated of by introducing into the equation for U the term 

— 2/111 cos a-j- , and into the equation for V, 2u2 cos a-- , where I de- 
dt at 

pends on the strength of the magnetic force, and a is the angle 

between its direction and the axis of z. 

From this it follows that the rotation is proportional to 

and the results of calculation agree fairly well with Verdet's experiments.* 
For the rotation of sugar terms of the same kind, but without the 
cos a, are introduced. 

It has been shown long since, by Airy,^ Neumann, and MacCuUagh, 
that such terms in the equations would lead to results in fair agreement 
with experiment, and Lommel does not attempt any other justification of 
their existence than that the results they lead to are in agreement with 
experiment. Similar remarks apply to his paper on the properties of 
quartz,'* in which the same terms are added to the differential equations 
already found for a crystalline media. The two waves travelling in any 
given direction inclined at an angle 6 to the axis are elliptically polarised. 
The elliptic paths of the particles are similar ; their ratio is given by — 

^ 6 8in2 0+ {62 8in<0 + <^o^cos''e]^ ' • ^^' 
and the difference of phase between the two by 

^2 = J2 sin4 a + (^^2 cos" fl . . . (61) 

where h and dg ^.re functions of the refractive indices and wave lengths. 
The axial rotation is given by — 

Q = c i^'-/) ' .... (62) 

' Lommel, ' Theorie der Dehnung der Polansationsebene,' Wied. Ann. t. xiv. p. 523. 
2 Verdet, Ann. de CUm. (3), t. (59, p. 471. 

' Airy, Phil. Mag. June, 1846 ; Neumann, Die mai/netischen Belmnngen, Halle, 
1863 ; McCuUagh, Roy. Irish Trans. 

* Lommel, ' Theorie der elliptischen Doppelbrechung,' Wied. Ann. t. xv. p. 378. 



ON OPTICAL THEORIES. 235 

These results are all in close agreement with experiment. 

In another paper ' this formula is carried to a higher degree of ap- 

proximation, and redaces to Q, = -^ — — — ^. This agrees well with the 

measurements of Soret and Sarasin, between the wave lengths 7604 and 
2143. 

§ 2. Ketteler's contributions to the theory of double refraction have 
been very numerous. Most of the papers already mentioned,- contain 
something on the subject. The theory given in the first of the papers 
mentioned is in its fundamental principles in close accordance with that 
developed by Lord Rayleigh in 1871, though the equations given on p. 95, 
following Von Lang, as representing the motion in a crystalline elastic 
solid are incorrect. In it a distinction is drawn between the displace- 
ment normal to the ray, which leads, it is said, to equations of the form — 

(m + mj^^+^=a'-^ht . . . (63) 

at- dx 

and those in the wave front, for which the equations are — 

^"^-■^i^^S) =''-"' ■ ■ ■ (•=*) 

The arguments by which the second equation is deduced from the first 
are somewhat obscure ; they are, however, further developed in a later 
paper.3 The ray direction is defined as that in which the energy of the 
vibration is propagated, and the direction of vibration is normal to this. 
The fundamental equations of this theory have already been given.* 
They are, in their final form,^ 






. (65) 



where the constants Cq, /3, k and y may all be functions of the direction. 
It IS shown in the paper (' Optische Controversen ') now before us that the 
conditions of incompressibility require that Co, k- and y should be constant, 
so that the theory turns entirely on the variability with the direction of /3, 
or rather of C, which is connected with Cq by the equation— 

C' = ^^.-Co (66) 

<■ n '^^^^ ^^ ^^*^^ ^° *^® groundwork of the theory, for in its form in the 

Optische Controversen ' it is assumed that C and Cq are unconnected. 

1 he paper ' Zur Dispersionstheorie ' starts wdthout the term in /3, 

arriving at the equation C + Co=0, and then (p. 208) inserts the /3 ' in 

^ ' Lommel, ' Das Gesetz der Eotationsdispersion,' Wied. Ann. t. sx. p. 578. 

■• p. 179 ; and also Ketteler, ' Zur Theorie der Doppelbrechung,' Wied. Aim. 
A t!™; ^; V ' ^^^°"e <^er absorbirenden Anisotropen-Mittel,' MonatsUr. der Konigl. 
Aitad. der Miss, zu Berlin, November 13, 1879. 

! ^etteler, 'Optische Controversen II.' Wied. Ann. t. xviii. p. 631. 

* See p. 228. 

* Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. sxi. p. 199. 



236 BEPORT— 1885. 

order to explain experimental results.' Introdacing the term C, as 
defined above, the equations become — 






(67) 



These equations will not lead to satisfactory results. 

Circular ' and elliptic polarisation are also treated of by Ketteler, and 

are explained on the supposition that terms of the form — Av + %-^\ 
come into the equation for U, and terms + (l\} + g^") into that for V. 

The rotation in a magnetic medium is given by ti = ir p ~ ' ^ N being 

the refractive index, while the value of N in a crystal like quartz may 
be found from the formula — 

W-\ = (N,2 _ 1) (1 + cos^fi) + (Na^ _ 1) sin2 « ± [(Nj^ - ■^^^) sin* 
+ 4fc2A2cos2 0(N,2_l)(N,2cos2« + N22sin2<9-l)]'. . (68) 

Ni and Nj being the refractive indices at right angles to the axis, and A;, 
a constant on which the rotatory power depends. For ordinary active 
media the law of the rotation is 

" = a+^2 + ;^4 + .etc. . . . (69) 

It will be noticed that in the theories of both Lomrael and Ketteler the 
rotatory terms are introduced into the equations of the matter particles, 
and affect the ether only indirectly through the values of «, v, and w. 

§ 3. Voigt's work ^ embraces double refraction and circular polarisa- 
tion. The existence of three principal axes is assumed, and for these the 
coefficients o and s in the values of /j and /,* of equations (53) vanish. 
The values of /^ and/7 are written down with coefficients a^, aj, etc., and 
a,', tta', etc., respectively, and finally the equation of motion for u is 
obtained in the form — 

"*" ^"^ + ^'^ ddy + ^'^ + ^-^J^z "^ £ [similar terms with a/, etc.] (70) 

It will be seen that there are enough coefficients here to give any 
imaginable theory of double refraction. 

Put m + r, = «i,, etc. Then the equations may be written 

> Ketteler, ' Theorie der circularen und elliptiscben polarisirenden Mittel,' Wied. 
Ann. t. xvi. p. 86. 

" ' Theorie des Liclites fiir vollkommen durchsichtige Median,' ]\'ied. Ann. t. xix. 
P- 873. * See p. 231. 



ON OPTICAL THEORIES. 237 

Where A, = A, + A/— 5, A; and A,' being functions of a, h, c, etc., and P 
ar 

cLtt 
is a linear function of p and the differential coefficients ^-, etc. 

ax 

The equations in this form may be compared with Green's, which differ 
from them only in the facts that his coefficients of drujdt^, cPy /dt"^, and 
d'^z/dt'^ are the same, and his other coefficients are independent of the 
time. Voigt's equations, in fact, include both Green's and those given by 
Lord Rayleigh. 

Let r be the period of vibration, and denote ?h, — n^T- by Tj, etc. ; then. 

it is shown that if we assume the relation — + — - + — = 0, in order to 

ax ay dz 

obtain Fresnel's wave surface at all the condition T, = T2 = T3 = Tia 

necessary. 

These equations being satisfied, the other relations required to give 
Fresnel's construction on either assumption as to the connection between 
the plane of polarisation and the direction of vibration are those given by 
Green, with the addition that since in Voigt's coefficients the period is 
involved, and since Fresnel'a construction holds for all wave lengths, each 
of Green's relations splits into two. 

A difficulty as to the meaning of the constants leads Voigt to prefer 
Neumann and MacCullagh's theory as to the position of the plane of 
polarisation. To obtain Fresnel's original construction it is necessaiy to 
suppose B]2 to be different from B21, and this would imply that elastic 
reactions are bi'ought into play by rotating an element of ether as a whole 
without dilatation ; that, in the ordinary notation of elastic solids, T,j^ is 
different from T,j,. If we treat this as out of the question, then B12 must 
be equal to B.,], and Fresnel's original construction for the plane of polari- 
sation is impossible. 

Circular polarisation is explained by the terms introduced by/2, /4,/g, 
and/^ of above,' but the terms to which /j and /g would give rise are 
omitted as not necessary to explain any known phenomena, and the 
equations in an isotropic medium become — ■ 

, , .d'^U f , ^dHl, . , d^U , dv , p'dH /^,n^ 

(.^ + 0^2 = («--),-^+«;p^.-'- + ^^+<7^, • (72). 
etc. ; the rotation produced by a thickness c of the medium will be — 



Q.— 



!V(e + a)(m + r- 



)V rvJr'^2(e + a)r2J- 



The same terms are then applied to a crystal, and the case of a uniaxial 
crystal such as quartz is worked out in full. 

The equation to determine the velocity in a direction making an angle 
6 with the axis is found to be — 

a and h being the velocities at right angles to the axis. 

This paper then gives a consistent account of the propagation of light 
in all known transparent bodies. We proceed to deal with the problem 

' See p. 231. 



238 REPORT— 1885. 

of reflexion and refraction on this theory, and after that to make some 
general remarks on the whole. 

Chapter III. — Reflexion and Refeaction. 

§ 1. Lommel, so far as I am aware, has not considered the problem 
of the reflexion and refraction of light on his theory. Ketteler, however, 
has discussed it in many of his papers. 

In one of the earlier papers ' the fundamental principles on which he 
intends to work are laid down. They ai'e as follows : — 

I. The conservation of energy. 

Ila. The continuity of the stress pai'allel to the surface of separation. 

116. The continuity of the component of the force on an element 
resolved normal to the surface. 

III. The continuity of the displacement resolved along the surface. 

The reasons given for 116. in place of the correct principle of the 
continuity of the stress normal to the surface are not very clearly stated. 

No assumption, except such as is implied in I. and III. combined, is 
made as to the displacement normal to the surface. 

The principles are then applied to the general problem, but in express- 
ing them in symbols, except in the case of I., the motion of the matter 
is entirely neglected. Thus the stress considered in II. is only that 
arising from the action of the ether ; the part which springs from the 
reaction of the matter is omitted from consideration. Again, in forming 
the equations connecting the amplitudes of the incident reflected and 
refracted rays, 116. is not employed. 

Ketteler's work, then, in this paper is not really specially connected 
with his theory of the mutual reaction between the ether and matter. It 
is rather a modification of Fresnel and Green's work, for which there 
can be no justification assigned. The problem of metallic reflexion is 
discussed, and in a second part ^ of the same paper that of moving media. 
In the next paper on this subject ^ the correct principle of the continuity 
of the stress normal to the bounding surface is introduced in place of one 
of the other conditions, but it is supposed that the term involving the 
dilatation disappears in consequence of the incompressibility of the ether ; 
in reality, as Green showed, the coefficient of that term is very large, and 
it must be retained to give correct results. Ketteler fails to see this, and 
hence concludes that the retention of Green's longitudinal wave is 
unnecessary. He then considers, as Green had done, the problem of total 
reflexion ; and, through not taking into account the continuity of the dis- 
placement normal to the surface, appears to be able to do without the 
longitudinal waves. The motion of the matter particles does not come 
into consideration. 

Another series of surface conditions are given in the next paper on the 
subject,'* and the matter particles being treated merely as a sort of 

' Ketteler, ' Beitrage zur einer endgiiltigen Festst^Uung der Sch-wingungsebene 
des polarisirten Lichtes,' Wied. Ann. t. i. p. 206. 

' Ketteler, Wied. Ann. t. i. p. 5.56. 

' Ketteler, ' Zur Theorie der longitudinalen elliptisclien Schwingnngcn im incom- 
pressiblen Ether,' Wied. Ann. t. iii. pp. 83, 284. See also Theoretisclie Optili, p. 130. 

•• Ketteler, ' Ueber den Uebergang des Lichtes zwisclien absorbirenden isotropen 
nnd anisotropen Mitteln und iiber die Mecbanik der Scbwingungen in denselben,' 
Wied. Ann. t. vii. p. 107. 



ON OPTICAL THEOEIES. 239 

ballast, their motions do not come into the surface conditions. "While, 
finally,' Ketteler adopts the principle enunciated by Kirchhoff,^ and 
already discnssed above,^ viz. that no work is done by the action of the 
stresses in the media on the bounding surface. In applying this principle 
he equates to zero, as Kirchhoff has done, the terms involving the dilata- 
tion ; and this, as has been already shovs^n, leads to MacCullagh's formulae 
on his assumption as to the equality of the density in the two media, and 
to Fresnel's if the rigidity be assumed equal in the two. The theory is 
applied to metallic reflexion and total reflexion within crystals in another 
paper.^ Thus, while Ketteler's first theory ^ was in reality Green's 
erroneously altered, this second theory is that given by Kirchhoff" in the 
paper ah'eady quoted. Neither of them really seems to me to involve the 
distinctive features of Ketteler's theory of the propagation of light. 

§ 2. Voigt's theory is contained in the paper already referred to.^ 

The conditions assumed are : — 

I. The displacement of the parallel to the surface ether is continuous 
in the two media. 

II. The displacement normal to the surface multiplied by the density 
is continuous.^ 

III. Kirchhoff"s principle — viz. that the work done by the stresses on 
the interface of the two media vanishes. 

In evaluating the expression for this work Voigt takes into account 
correctly the terms arising from the action of the matter on the ether. 
The displacements which come into the equations expressing the first 
two conditions are strictly displacements of the ether relatively to the 
matter, but since it is assumed that the motion of the matter particles 
is very small compared with that of the ether, the absolute displacements 
of the ether particles are introduced. 

The results arrived at, however, are hardly satisfactory. In the first 
place, in evaluating the expression for the work done on the surface, the 
term involving the dilatation is omitted. Voigt has taken it into account 
in his equations of motion ; his reason for omitting it here is not given. 
He thus avoids the question of the so-called longitudinal vibrations. 

_He then considers the case of vibrations at right angles to the plane 
of incidence, and arrives at the formulae — 

E, + R, = D. . 

(^1 4- r, - ni !-2) (E, - R,) sin^j cos^i ■ . . (74) 

= (wi2 -t- r.j — «2''^) Dj8in02cos^2 ■ 

B, R, and D being the amplitudes of the incident reflected and refracted 
waves. 

' ' Ketteler, ' Optische Controversen II.' Wied. Ann. t. xviii p 632 

'' Kirchhoff, Ahhandl. der Berl. Ahad. 1876, p. 57. 

' See p. 193. 

* Ketteler, ' Ueber Problems welche die Neumann'sche Eeflexionstheorie nicht 
losen zu konnen scheint,' Wied. Ann. t. xxii. p. 204. 

' See p. 162. 

« Voigt, ' Theorie des Lichtes fur vollkomnien durchsichtige Median,' Wied. Aim. 
t. XIX. p. 873. See also Voigt, ' Ueber die Grundgleicbungen der optischen Theorie des 
Merrn E. Ketteler,' Wied. Aim. t. six. p. 691, especially p. 696 sen. 

' See p. 186 ; also Cornu, Ann. de Chim. (4), t. xi. p. 283. 



240 EEPOKT— 1885. 

These become MacCullagh's and Neumann's formulas on the assumption 
that 

???, +ri = ?Ho + r, ) 

- - . . . . (75) 

They become Fresnel's if 

' ... (76} 



' I 



a\=a 

for these equations lead — remembering the value of the velocity — to the 
condition — 

m^ + ^1 — WjT^ _ sin 2^ 2 

m^ + r^ — ^2^^ sin^0, 

For the vibrations in the plane of incidence the results of the first and 
second principles are inconsistent with that of the third. For the first 
and second give 

(E„ + R^) cos^i = DpCos^)2 ) 

771 1 (E^ — R,,) sin ^ 1 = mj D,, sin ^2 > 

while the first and third give, instead of this second equation, 

(to, + r, — H., r^) (Ep — Up) sin*! = (wg + ?'2 — "2'') Dp sin02 • (78) 

They become consistent If Ave assume mi ^7^21 ^^d, adopting Neu- 
mann's hypothesis, 

r, = r2. Ml ="2, 
or, adopting Fresnel's, 

ei+ai = e2 + a2) ci''i=ct'2- 

In another paper' it is shown that KirchhoflT's principle, when applied 
to circularly polarising media, leads to an impossible result, and the 
principle is modified by the supposition that the work done is a function 
of the time only, and not zero. 

The theory of ordinary absorbing media is developed ^ from the 
supposition that terms involving a loss of energy may come in through 
the mutual reaction of the ether and matter, and it is shown that these 

would lead to terms of the form — t — - + cv^-, in the equation for 

at at 

u, which merely becomes, for waves travelling parallel to z, 

where 

(80) 

In considering the problem of reflexion in this case, Voigt assumes 
that the plane xy being the face of incidence, Mtw is continuous. The 

' Voigt, ' Das G. KirchhoflE'sche Princip und die Tlieorie der Reflexion und 
Brechiing an der Grenze circular-polarisender Medien,' Wied. Ann. t. xx. p. 522. 
^ Voigt, ' Theorie der absorbirenden isotropen Medien,' Wied. Ann. t. xxiii. p. 104. 



M. 


dH 
dt^ 


= A, 


dho 


— 


,du 

^d! 


+ ' 


^dzm 






M.= 


:«l, 


+ 


'"i - 


"•1 


r 






A,= 


= e, 


-4- 


«i - 


a', 
72 


f 
] 



ON OPTICAL THEORIES. 241 

principle laid down in the former paper ' would require that this should 
be mw, not Mw, as he points out, remarking that the equation given is only 
true under certain restrictions, and, in fact, he shows that for vibrations 
in the plane of incidence the continuity of Mw is inconsistent with the 
energy equation, at least unless & = 0. The energy equation gives 

M.,w,=^L,w._-h^T^- I . . . (81) 

and this form is assumed for the rest of the work. 

Expressions are then found for the difference of phase between the 
reflected, refracted, and incident beams, and for their relative intensities, 
and these are compared with theory on the assumption that the con-' 
stant h vanishes, and that Mj =M2. The results of the comparison are 
satisfactory; but this, however, can hardly be said for the principles 
from which they are deduced, while the difficulties we have already 
alluded to as to the negative value for the real part of the square of the 
refractive index remain in their full force. 

Chapter IV. — Theoet of Sir "William Thomson. 
General Considerations. 

§ 1. The lectures of Sir William Thomson delivered last year at 
Baltimore have developed a new interest in the theories now under con- 
sideration. After discussing at some length the elastic solid theory and 
throwing much light on it, and on the meaning of the twenty-one 
coefficients of Green's theory, he points out its unfitness to explain the 
phenomena, and then proceeds to work out the consequences of a special 
form of reaction between the ether and matter ; this he illustrates in his 
own inimitable manner by his mechanical model of the ether within 
a transparent body. This mechanical model consists of a number of 
concentric hollow spheres. Each sphere is connected with the one 
withm it by zigzag springs, and in the centre there is a solid mass 
connected also by springs with the shell next to it. The dimensions of 
these shells, which represent the matter molecules, are supposed to be 
small compared with the wave length. The interior molecule will have 
anumber of periods of vibration depending on the number and nature 
of the spring connections, on its own mass, and on the masses of the 
shells. The springs are supposed to be massless. The shell molecules are 
distributed through the ether in very large numbers, and the outermost 
shell is connected with the ether. 

It is further supposed that the forces arising from the springs are 
proportional to the relative displacements of the centres of the shells, and 
that the ether acts on the first shell with a force proportional to the 
relative displacement of that shell and the ether surrounding it, so that, if 
4 be the ether displacement, .^,, Xo those of the shells, mJ4,7r'\ m^/47r^, etc. 
their masses, the equations of motion are, 



m. 






4^2 -^ = <^2 (2^1 - aJa) - C3 i^i - X3) 

' Voigt, Wied. Ann. t. six. p. 900. See above, p. 239. 
looo. 



(82) 



E 



242 EEPOET— 1885. 

etc. If we suppose the whole motion to be harmonic and of period t, then 
the equations become 

-^f^i = G,{i,-x^)-C^{x,-x^) . . . (83) 

etc., from which the motion of the various shells can be determined. 
The system will represent Helmholtz's theory if we suppose the viscous 
terms in his expression to vanish, and consider only a single shell. The 
solution in the general case is carried further by putting 



and ^^._ _ C,x,-, 

The equations may then be written — 

u 



• (84) 



Wj = tti 



«2 = ^2 — ^'^ 



(85) 



"-s / 



etc., whence we find Mj as a continued fraction. 

By differentiating these expressions with reference to t~^, and writing 

^ for -, we find — 

Su, = 7», + (9i±l ] w .^ , + (^i±&A \^^ + , etc. . . (86) 



Hence 

J^'=-73^7{-^^^.^ + -.>.-^>l+ • • • •} . . (87) 

Thus tt decreases as r increases, and if we start from r, a small quan- 
tity, the us are all large and positive ; hence alternate shells are movincr 
in opposite directions, and the motion of consecutive shells rapidly 
decreases. 

As r increases the ii's decrease, and after a time one will become 
negative, passing through zero — it can be shown that ttj is the first oije 
thus to become negative. This gives the first critical case in the solution, 
for then re, is infinitely great compared with ^, and the solution fails. 

This equation can be put into the following more convenient form — 

.^=li{jM^+Ji|!^ + . ...}.. (88) 

where c,, (C2, etc., are the critical values of r, and R,, Rg, etc., represent 
the ratio of the energy of the several shells to the whole energy of the 
system. 

To apply this to the motion of the ether in a transparent body, let 
«ii/47r2, etc., represent the whole mass contained within shell No. 1 per 
unit vol., let p/47r2 be the density, and el^v"^ the rigidity of the ether, aud 
suppose the first shell, of mass m,, to be connected by a spring to a massless 



ON OPTICAL THEORIES. 243 

spherical lining, which is in rigid connection with the ether outside. 
Then the equation of motion is — 

Let the solution of this represent a train of waves of period r and 
length X, and let V be the wave velocity for the medium. Then 

and if n be the refractive index, since the velocity in free space is y/ ejfj 
we have, if we put Ciki^Ri=g',mi, etc. 

P L 
+ gi-^i^ fe + TT +••••) ~ *®^™^ ^^22, ?3 I . • (91) 

It follows from this that, ji must be very little less than unity if the 
formula, neglecting the terms in q^, etc., is to apply to a transparent sub- 
stance such as rock salt, which gives a value for^ between 1 and 2 for 
a range of the spectrum from the visible light to the longest waves emitted 
by a Leslie cube. The formula, we note, is the same in form as that 
given by Ketteler and Biuot (see above, page 181), and Ketteler has 
shown that in some fairly transparent substances the coefficient 1 — ^i is 
appreciable, gi ^s essentially less than unity, so that the term in r^ comes 
in with a negative coefficient. The formula, then, will explain ordinary 
■dispersion fairly if we put q2, 23) ^tc., all zero and take r greater than ki. 

The critical cases are then discussed from the form 

In this, r is greater than k\ and less than /cj for ordinary refraction. 
As r decreases down to k^, jj? passes through the value infinity and then 
becomes negative, we have greater and greater refraction, and then the 
waves cease to be transmitted and absorption takes place. 

And here we are met with the question — What becomes of the energy 
thus absorbed ? According to our equation the ratio a;, jl becomes infinite, 
and the solution as it stands fails to meet this difficulty. Helmholtz 
introduced the term —y'^dJJIdt into the motion of the first shell, and this, 
representing as it does a viscous consumption of energy by the matter 
rnolecules, is objected to by Sir Wm. Thomson. Helmholtz's solution 
given on p. 221 becomes identical with that at present under discussion if 
we put y=0 ; it is to meet this case in which t-^c, that the term in y* is 
introduced, for if k represent the co-efficient of absorption on Helmholtz's 
theory, and we suppose y to be small, then, with Thomson's notation, 

•v2t< 
(t* - Ki2)» 

very approximately, K being a constant, and Jc may be very small except 
when r is nearly equal to k^. 

B2 



h' 



244 EEPOET — 1885. 

In order to acconnt for the extreme transparency of a substance such 
as water, we must suppose h to be so exceedingly small that Sir 
William prefers to consider it as zero, and says : ' I believe that the first 
effect when light begins, of period exactly equal to c,, is that each 
sequence of waves throws in some energy into the molecule. That goes 
on until somehow or other the molecule gets uneasy. It takes m, 
(owing to its gi-eat density relative to the ether) an enormous quantity 
of energy before it gets particularly uneasy. It then moves about, and 
beo-ins to collide with its neighbours, perhaps, and will therefore give you 
heat in the gas if it be a gaseous molecule. It goes on colliding with 
other molecules, and in that way imparting its energy to them. This 
energy is carried away (as heat) by convection, perhaps. Each molecule- 
set to vibrating in that way becomes a source of light, and we may thus 
explain the radiation of heat from the molecule after it has been got intO' 
it by sequences of waves of light.' 

Helmholtz's equations are, of course, the more general, and apply to- 
an absorption band as well as to the part of the spectrum for which the 
medium is transparent. It would seem that the term —y^dU/dt may 
rightly represent just the effect of that loss of energy in the form of 
heat due to the irregular collisions of which Sir William speaks, an 
effect which is only appreciable in the result when, owing to the 
coincidence of the periods, U tends to become large compared with u, or,, 
in Thomson's notation, Xi large compared with ^, and in this case x^ will 
not become infinite, for the amplitude will be multiplied by the factor 
e-*^', and k being large, the limit of the product comes into consideration. 

Such a system oF ether with attached matter molecules is thus shown 
to account for the phenomena of dispersion. A serious difficulty, how- 
ever, is encountered when we reach the problem of double refraction. 

§2. For we may suppose, in order to account for it, that C, is a func- 
tion of the direction, and that for two principal directions it has the- 
values Ci and C/, while C2 is a constant independent of the direction. 

Then, with only one enclosed mass, 

h - Co) 

,, = l + C^All ±, .... (93) 

and to give a dispersion formula resembling Cauchy's we must have 

7Hi/-2 considerable compared with C2,_and Ci large compared with either. 

Hence, if /i' be a second principal index, 



//2=1 + 



C 






and therefore r'^fc — — -^ 



p (c, + c,-^')(c/ + c.-5-) 



which, remembering the relative magnitudes of the quantities, and writ- 
ing Dand D' for the approximate values of the denominators, becomes 



ON OPTICAL THEOKIES. 245 

60 that the difference between the squares of the refractive indices will 
be inversely proportional to the squares of the wave length, and this is 
quite contrary to experiment. The question as to whether the theory 
here suggested would lead to Fresnel's construction is not considered. 

In a later lecture Sir "William returns again to the question of what 
becomes of the energy absorbed by the molecules, and of the nature of 
the ether. As to the latter he adopts Stokes's view, that the medium may 
be perfectly elastic for the small disturbances of a light-wave, executed, 
as they are, in the twenty-million-millionth of a second, and yet be a 
perfect fluid in respect of forces which act, as may be supposed in the 
kinetic theory of gases, for the one-millionth of a second. Now, the 
numerical calculations of Professor Morley, undertaken at Sir William's 
suggestion, show that the energy given to a system such as described 
tends to become absorbed by the vibrations of lower modes, so that the 
original energy appears as vibrations in which the period may be the 
millionth of a second instead of, perhaps, the twenty-million-millionth, and 
this energy shows itself in the motions which we deal with in the kinetic 
theory of gases, rapid it may be in themselves, but slow compared with 
the light- vibrations. 

§ 3. Metallic reflexion and the quasi-metallic reflexion of such sub- 
stances as give anomalous dispersion are dealt with, and it is shown that 
the phenomena are such as would be produced by making jx^, a negative 
quantity, and this is given by values of r a little below the critical period. 

Thus the molecular explaaation of the great reflecting power of silver 
is that the highest mode of vibration of the molecules with which silver 
loads the ether is graver than the mode of the gravest light or radiant 
heat which has ever been reflected from silver ; and if, again, for certain 
modes /x^ is not negative, but less than unity, it shows that, conformably 
with the experiments of Quincke on gold leaves, we should expect light 
to travel through the medium faster than through air. This forms a 
marked and most important distinction between this theory and others 
which have been given to explain metallic reflexion. For the other 
theories the metallic effects arise from the importance of the viscous 
terms of the form —ydujdt. 

In an appendix Sir William works out the problem of reflexion and re- 
fraction, following Green and Lord Rayleigh so far as ordinary transparent 
media are concerned. He then transforms Green's formute for vibra- 
tions in the plane of incidence to the case in which /x^ is a real negative 
quantity, and arrives at formula expressing, on a strict elastic solid 
theory, the intensity and change of phase in a wave reflected from metal. 

According to this solution we have, if v"^ = — fx^ so that v^ is positive, 
the values of * and ^ given by — 

* = — >'^ cos (aa!-|-&y + w<) + tan fl!^^*— ^tL_i_ sin {ax + 1]! + ut) 

*i= — v^cos{ax + hy + ut)—\ja.nd ^^'''^ ' sin ( + aa.' + &y + wQ 

r^ — 1 

. vVj'2 + 1^ , . , \. (95) 

^ = - ^^ _^' e-"^ sin (by + wt) 1 ^ ' 



*' = _ ('-' + !) 



v'-l 



bx 



sin (ly + ut) 



246 REPORT— 1885. 

These are simplified if we put — 
A2 = ((,.2 + 1) 52 + ,,2^2} r^ + tan B Q^^t^l , 2 = tan/ 

S = v^ sec/ 



(96) 



and the displacements in the transparent medium are then, for the incident 
wave, 



and for the reflected. 



— — S sin (ax + hy + wt +/), 

A 

-— S sin (— ax + ly -{■ wt — /). 
A 



In this case the rigidities in the two media are supposed to be equal. 
Sir William has also worked out the problem in the case in which the 
rigidities are not equal, in the hopes that by this assumption combined 
with variations in the density — or rather effective density — the variations 
from Green's formula in the case of light polarised at right angles to the 
plane of incidence may be accounted for. He finds, however, that, 
any difference of rigidity which might, combined with a difference of' 
density, be sufficient to reconcile Green's theory with experiment would 
cause the proportion of light reflected at normal incidence to be greater 
than {(/u — l)/(/j + 1)}2, and this value, given by Green's theory, 
agrees closely with Rood's experiments. We are thus driven back to 
Lord Rayleigh's case of equal rigidities in the two media. For metals, 
then, we are to have the rigidities equal, and the value of ^i^ decreasing' 
from — 00 when r = /.i to zero when r = /.-, /N, N being some lai-ge nume- 
rical quantity, and then again augmenting from zero to unity as r 
decreases from kJ'N to 0. ■ 

The dynamics give no foundation to a theory such as Cauchy's, in 
which n' is a complex quantity. For light polarised in the plane of inci- 
dence we have, if n and n be the rigidities, and 

r = n'/n, ) 

... (97) 
and tan e = i-(i -sec^^^ + tan^ej^j 

R = i (H- r2(v2sec2 -I- tan^e)} ^ 

4 = R cos {ax + by+o)t — e) i . . . (98) 

^= R cos (— ax + by + wt + e) ) 

for the incident and reflected wave ; and for the refracted wave, 

f = /T^(-^ + ^"'=«^-cos(%-FwO . . . (99) 

According to these formulaj the reflexion is total from a metal surface at 
all angles of incidence. Sir John Conroy has recently shown that the 
loss is exceedingly small. If light be polarised in any plane, then the 
vibration in the plane of incidence is retarded relatively to that at right 
angles to that plane by the amount 2f+ 2e — tt. If we suppose v and rv 
to be both very large numerics, this retardation becomes — 



ON OPTICAL THEORIES. 247 

and from the observations wliicli have been made on the value of the 
principal incidence, for which the retardation is ^tt, we can find a value 
for rr. For silver Sir J. Conroy's observations give (rv)~^ = 3'65. 

And here we are met with a great difficulty. Experiments show that 
there is very little chromatic eflPect about metallic reflexion. Thus, since 
the value of the principal incidence depends mainly on ry, this quantity must 
be independent of the period. Now v^ + 1 is approximately proportional 
to T^ when r is small compared with Ki, and so this result requires that r, 
which is proportional to the effective rigidity, should also vary in a certain 
definite manner, and it is difficult to see how the theory is to give this. 

The theory is then applied to the case of a thin metal plate, and leads 
to the fact that the phase of both components is accelerated by the 
transmission. The accelerations for the two cases are given by — 

c cos ^+( — — — l^^, vibrations normal to the plane of incidence, 

d cos 9 + ( T~ — ) \ vibrations in the plane of incidence, 
V4 Try 

when S is the thickness of the plate, and e and /are found in the same 
manner as above. 

This acceleration was discovered by Quincke, but the details of his 
results do not agree well with the formulas. The formulas are consistent 
with Kerr's discovery of the rotation of the plane of polarisation by 
reflexion from an iron plate when magnetised, but not with Kundt's 
result that transmission through a thin plate of iron in a magnetic field 
produces a very large rotation of the plane of polarisation. 

In a final appendix an account is given of a gyrostatic molecule, the 
properties of which would give to the medium the heliacal effects seen in 
sugar and other active solutions. The molecule consists of a spherical 
shell in which are imbedded two gyrostats having a common axis, which 
initially is a diameter of the shell. One end of each axis is connected 
with the shell by a ball-and-socket joint, while the second extremities of 
each are connected together at the centre of the shell by a second ball- 
and-socket joint. 

§ 4. Having thus given an account of the various theories proposed 
based in some way on the mutual reaction between th,e ether and matter, 
it remains to compare and contrast them. 

The theories of Boussinesq and Voigt have much in common, and 
neither of the two as they stand applies to the case of bodies showing 
strong absorption, for the matter motion is entirely neglected. The theo- 
ries of Sellmeyer, Helmholtz, and Thomson come under one head in 
that they all make the mutual reaction to depend on the relative dis- 
placement of the matter and ether. 

Lommel's theory seems to me untenable : in its original form it con- 
tradicts the third law of motion, and if modified so as to be consistent 
with that, it leads to impossible laws for the relation between refraction 
and absorption ; besides this, his theory of double refraction does not 
lead to Fresnel's wave surface, and there seems no reason why the co- 
efficient a^, which occurs only in the equation of motion of the matter, 
should be the one to be treated as a function of the direction. The laws of 
circular polarisation and of the double refraction in quartz, to which the 
theory leads, and which seem to agree with experiment, may be obtained 



248 



EEPOKT 1885. 



with sufficient approximation to fit the experiments from other theories ; 
and, indeed, the fact that the wave surface in quartz does not become a 
sphere and a spheroid when the heliacal terms are neglected is fatal. 

"With regard to Ketteler's theory in the form finally given to it by its 
author,' it seems to me to have no possible mechanical basis. With the 
interpretation which he gives of the constants involved, his equations 
appear to contradict Newton's third law as effectually as do Lommel's, 
while, so far as the problem of reflexion and refraction is concerned, I 
cannot recognise the validity of Kirchho0"'s principle as it is applied by 
Ketteler. At the same time I think that the suggestion of Ketteler — to 
which, however, he himself takes objection— already mentioned, leads 
to results which, so far as dispersion is concerned, agree closely with 
experiment. 

We may with advantage compare the dispersion formula which it 
gives with that which comes from the theories of Helmholtz and Thomson. 
If we neglect the terms depending on viscous action, we have, accord- 
ing to Helmholtz, for ^, the refractive index, 

( \* ^ 



:1- 



pXi 



f""i 



^1^ 



^-1 



(100) 



while, according to the modified form of Ketteler, 

f ° 



5 '■ 



1 + S U2 



1— - 



(101) 



Ketteler's equations come from Thomson's or Helmholtz's by writing 
for C, the quantity — 4^20, /r^, or for /j^ in Helmholtz's notation — n^pi^. 
We may write Ketteler's equation in the form of a series thus — 

=^l [l+lD{*f + j^;*+ ....}] . (102) 

two terms of which will give us Cauchy's series with three constants. 

This modification leads also to an escape from one of the difficulties 
suggested by Sir William as to the explanation of double refraction. 

For his general expression for yu^ will become, if we write for Cj the 
value -4T2Ci/r2, 

47r2C, 



yu2 = l + 






+ 



•)} 



(103) 



If we neglect for a moment the terms on which the dispersion depends, 
as being small compai-ed with the term 4-Tr^Cilp, which gives rise in the 
first instance to refraction, we get that 



4^r2(Cj-C/) 



(104) 



and there will be double refraction independently of the period. 

' Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199. 



ON OPTICAL THEORIES. 249 

It is another question, and one which we shall discuss shortly, whether 
the double refraction thus produced will give rise to Fresnel's wave surface. 

There seem, then, to be reasons why we should expect terms such as 
Ketteler has suggested in our equations — terms which will make the mutual 
reaction of the ether and the first matter shell depend rather upon their 
relative accelerations than upon their relative displacements. It is not so 
€asy to suggest a mechanical connection between the ether and matter 
which would give rise to this force, but at the same time there is, I 
think, no mechanical reason to be urged against it. 

Voigt's theory of wave propagation is in one way more comprehensive 
than those we have considered, while in another it is less so. It is more 
romprehensive in that it includes both sets of terms with some others in 
the expression for the mutual reaction ; it is leas so in that it treats the 
ratio U/m as a small quantity which may be neglected. This same 
remark applies to Boussinesq, whose work in one sense is more general 
that Voigt's, in that he considers the efifect of the attached molecules on 
the condensational or pressural wave. 

The presence of these molecules has been shown in Bonssinesq's 
paper to alter the effective compressibility of the medium as well as its 
density and its rigidity. In the ether we assume that the compressibility 
is small compared with the rigidity, so small that the ratio of the two 
may be neglected, and this must still be the case, even when the ether is 
loaded. But when dealing with the problem of reflexion we are concerned 
with the refractive index of the medium for the condensational wave. 
This will depend on the ratio of the two effective compressibilities, as 
well as on that of the two effective densities, and though either of the 
two compressibilities may vanish when compared with the rigidities, in 
considering their ratio it becomes necessary to take into account any 
change due to the loading of the ether. 

It may not be unreasonable, then, to suppose that the effective density 
of the ether for the condensational wave is different from the effective 
density for the transverse wave. This supposition would account easily 
for the variation from Green's formula observed when plane polarised 
light polarised at right angles to the plane of incidence is reflected from 
a transparent surface, in that it would allow us to introduce the second 
constant jjq, as suggested by Haughton and Lord Rayleigh.' 

Let us now consider Voigt's theory. With regard to the problem of 
reflexion his surface conditions appear to be unsound. The ether is the 
continuous medium, and the surface conditions must apply to it simply. 
The conditions of continuity demand that the actual displacements of the 
ether and the actual stresses over the interface, arising, of course, in part 
from the action of the matter, should be the same in the two media. 
The validity of Kirchhoff's principle has already been considered, and it 
has been shown that it does not lead to results in accordance with experi- 
ment, for it does not give the change of phase which in some cases 
accompanies reflexion. 

But, while this is so, Voigt's theory shows us that the effects of the 
attached molecules may show themselves either in the rigidity or the 
•density of the ether. Now, the work of Lord Rayleigh and Lorenz has 
proved that the effects of reflexion are due mainly, if not entirely, to 
differences of effective density ; and so we must look to the terms in 

' See p. 192. 



250 BEPOET — 1885. 

Voigt's theory whicli aflPect the density as the most important. These 
terms are 

_(,g,+ „)(„-U). 
The other terms, 

show themselves as a variation of the effective rigidity. In order to 
obtain a consistent theory of reflexion we must treat these as of secondary 
importance compared with the first terms. Now, this is inconsistent with 
both theories of double refi-action as advanced by Voigt, for the first 
condition for either is that r and n must be independent of the direction. 
It would seem from this that they should be the same in all media. 
Boussinesq adopts the opposite view. He makes his double refraction 
depend on the terms which correspond to r and n, and neglects the 
variations of the others with the direction. If we do this — and we seem 
to be forced into it by the further requirements of our theory — the funda- 
mental equations in a crystal become those given by Lord Rayleigh. 
These, we have seen, if we assume the strict transversality of the 
vibrations, do not lead to Fresnel's wave surface. On the other hand, if 
we suppose that the vibrations in a crystal are at right angles to the 
ray, not to the wave normal, the result agrees with all the consequences 
of experiment, for we obtain Fresnel's surface as the wave surface, but 
we are left in a difficulty as to the normal wave. 

With regard to metallic reflexion, the theory as given by Sir "W. 
Thomson explains completely the difficulty raised by Lord Rayleigh as to 
a negative value for ^^. It does not, however, enable us to decide how 
much of the effect is due to the fact that the highest possible free period of 
the ether in the metallic medium is below that of the incident light, and 
how much is due to opacity arising from terms such as dujdty&s supposed 
by Lord Rayleigh. The correct equations to which such a theory would 
give rise are yet unsolved, but the principles required by the solution are 
well known. 

It seems, then, that this theory promises to afford us the solution of 
the difficulties which still surround theoretical optics, and to account at 
once for the phenomena of reflexion and refraction, dispersion and double 
refraction. Of course, in all cases of transparency the matter motion is 
infinitesimally small compared with that of the ether. The ether is to 
be looked upon as moving through a sort of network of fixed matter 
particles. Terms depending on the reaction between the ether and 
these fixed portions of matter will be introduced into the equations, 
and these terms will be expressible as functions of u, v, w and their 
differential coefficients. The matter particles will not move appreciably, 
and their movement is not necessary for the explanation of refraction and 
ordinary dispersion ; for on Ketteler's modified theory we have, if we 
omit the viscous terms, 



in rrifx (»'''* — «,*)' 
and the ratio of the amplitudes is 



/32n2 



fi(^v'^ — n'^) 



ON OPTICAL THEORIES. 251 

From the value of /i^ we see that y3^ must be comparable with m, the 
density of the ether, so that, except when «^/(»2 — ?t^) is a large 
quantity, the ratio of the amplitudes will be inversely as the densities, for 
l^^/fj will be comparable with mjij. When, however, n-j{_v^ — ii^) is 
large, the matter motion becomes appreciable, and the phenomena of 
anomalous dispersion arise. 

Part IV. 

THE ELECTRO-MAGNETIC THEORY. 

Chapter I. — Maxwell's Theory. 

§ 1. There remains now for consideration Maxwell's electro-magnetic 
theory. The fundamental equations of this theory are purely electrical, 
and are established on electrical principles. According to Maxwell, when 
electromotive force acts on a dielectric medium the change of condition 
known as electric displacement is produced. The two are connected by 
the equations — 

P = ^/, etc (1) 

P, Q, R being the components of the E.M.F. and /, g, h of the dis- 
placement. K is the inductive capacity. In a crystal the equation 
holds only for the principal axes, and along these K has three diiferent 
values. 

The rate of variation of the displacement given by/, g, h constitutes 
the current in the medium, and it is an essential part of the theory 
that — 

df do dh 

— + — + 

d.e dy dz 

vanishes everywhere. 

The current is connected with the components of the magnetic in- 
duction a, b, c by the equations — 

de dh . J ._, 

etc., and the magnetic force a, /3, y is given by 

a = fici (3) 

etc., where /i is the coefiBcient of magnetic capacity. 

a, b, c are also given in terms of a quantity known as the vector 
potential, the components of which are F, G. H, by the equations — 

fZH dG 

''=dy~^ ^^^ 

etc., and from these it follows that 

W=|^-V2F .... (5) 

etc., where 

j_ dF ^ dB. 

dx dij dz 



252 EEPOET — 1885. 

while the electromotive force at any point is also determined in terms of 
this same quantity F, G, H by the equations 

p_ dF d^ , 

etc., ^[' being the electrostatic potential. From this it follows that 

,K^(^+f)-v^F+.f-=0 .... (7) 
dt \ dt dx J ax 

etc., and the vector F travels through the medium with velocity 1/n/K^. 
Now, the value of this quantity can be determined by experiment, and 
agrees very closely indeed with the velocity of light. Thus the vector 
potential, and in the same way the electric displacement and the magnetic 
induction, travel through the medium with a velocity, as nearly as we can 
eay, identical with that of light. 

Moreover, the electric displacement corresponding to this is in the wave 
front, and the same is the case with the magnetic induction a, h, c. By 
this motion energy is conveyed through the medium, the electrostatic 
energy depending on the electric displacement, the electro-kinetic on the 
magnetic induction, and the two can be shown to be equal. Thus the 
theory agrees with the undulatory theory of light in assuming the exist- 
ence of a medium capable of becoming a receptacle of two forms of 
energy. Electric displacement and magnetic induction are, then, changes 
of condition which can be propagated in waves of transverse disturb- 
ances through the medium with a velocity practically identical with that 
of light. Maxwell's theory supposes that there is an intimate connection 
between the vibrations which constitute light and electric displacement ; 
according to some of his followers the two are identical, though, so far 
as I can judge, that is not necessary to the theory as he left it. 

Now, experiment shows that the value of /j. is nearly the same for all 
media, so that it follows that on this theory the specific inductive capa- 
city of a medium — the ratio of its inductive capacity to that of air — 
should be equal to the square of the refractive index. Experiments have 
shown that while this law is by no means true for all substances, it is suffi- 
ciently nearly so for many to render it probable that V K gives the most 
important term of the index. 

In estimating the value of the comparisons we must remember that 
while K is determined by observations lasting over an appreciable time, 
the refractive index depends on vibrations of great frequency ; to compare 
the two, then, we have to adopt some dispersion formula, and find the 
value of the index for waves of infinite period, and this alone is a source 
of error. 

Again, the equations for a crystalline medium are obtained by Maxwell, 
and he shows that the velocity of wave propagation is given by Fresnel's 
construction, while the electric displacement is in the wave front, and its 
direction is that of the axis of the ellipse which determines the velocity. 
The theory is not burdened with a wave of normal vibrations, and 
accounts quite simply for all the phenomena of double refraction. 

§ 2. The theory of reflexion and refraction of electro-magnetic waves 
was first given by H. A. Lorentz,' who follows a method of attacking the 

' Lorentz, SMomilch. Zeitschrift, t. xxii. 



ON OPTICAL THEOEIES. 253 

problem which is dae to Helmholfcz.' This we shall consider later. It was 
also solved by J. J. Thomson,^ so far as the isotropic media are concerned, 
and by Fitzgerald. ^ 

Some further developments of the theory are given in a paper by the 
author of this report, and read before the Cambridge Philosophical 
Society.* 

In this paper the general equations for the displacement and for the 
magnetic induction in a crystal are given. If a, b, c be the principal 
velocities given by the equation 

2 1 
3tc., then 



dt^ •' dx\ dx dy dz J ^ ' 



etc., while 



d'^n, -J (i^a TO d^a -^ d^a 



— i. ("a"^" +62^+0^^^ . . . (9) 
dx\dx dy dz ) ' 

If a wave of electric displacement S', in a direction in which the 
inductive capacity is K', be traversing the medium, the electromotive 
force is 4!7rS'/K' in the direction of displacement, and 4rrS' tan x/^' 
along the wave normal, when x is the angle between the ray and the 
wave normal. 

§ 3. The surface conditions implied by the theory, and used by Lorentz, 
J. J. Thomson, Fitzgerald, and Glazebrook, are that the electric and 
magnetic displacements normal to the interface are continuous, while the 
electric and magnetic forces in the interface are also continuous. 

The formulae obtained are identical with those given by MacCuUagh 
and Neumann, electric displacement being substituted for the ordinary 
displacement of the medium. 

The theory has the very great advantage over the ordinary elastic 
solid theory that reflexion and double refraction are both explained by 
variations in the same property of the medium, viz. the inductive capacity. 
Variations in its value from medium to medium give rise to reflexion and 
refraction ; variations in different directions within the same medium are 
the cause of double refraction. 

§ 4. The theory has been applied by Lord Rayleigh to account for the 
various phenomena ^ connected with the scattering of light by a cloud of 
small particles. These are deduced satisfactorily from the theory on the 
supposition that \i, the magnetic capacity, is a constant through the two 
media, and that the effects are due to variations in the inductive capacity, 
while, when terms of the second order in A K/K are included, the scattered 
light does not vanish — the incident light being plane polarised — in a direc- 

' Helmholtz, Sorchardfs Journal, Band Ixxii. 

"^ J. J. Thomson, Phil. Mag. April, 1880. 

» Fitzgerald, Phil. Trans. 1881. 

■• Glazebrook, Proc. Camh. Phil. Soc. vol. iv. p. 155. 

' Lord Rayleigh, ' On the Electro-magnetic Theory of Light,' Phil. Mag. Aug, 1881. 



254 EEPORT — 1885. 

tion normal to the incident light, but in one inclined at an obtuse angle 
to that in which the light is travelling. Tyndall observed this effect 
when the particles scattering the light cease to be very small. 

Chapter II. — Hei.mholtz's Theory. 

§ 1. Helmholtz looks at the problem of the propagation of an 
electro-macrnetic disturbance in a somewhat different manner, and a com- 
parison of the two theories is given by the author of this Report.' | 

The electro-magnetic effects in the medium depend, according to I 
Maxwell, on the values of F, G, H, the components of the vector potential, | 
or as Maxwell also calls it, of the electro-kinetic momentum, and if 
we integrate round a closed curve, the values of F, G, H satisfy the 
equation 

[Fdx + Gdy-B.dz = {{'^ dsda . . . (10) 

where ds is an element of the curve, i the current at any point at a 
distance r from ds, da an element of the curve in which the current i is 
running, £ the angle between (7s and da, and the integration on the right 
extends round the two carves s and a. 
From this we can show that 



And if we put 
we find that 



-4fli 



dx'dy'dz' +^ 
dx 



4^ + ^+^'=l-v2* 
dx dij dz 4- 

V 2F — — - = — 47r/i/ + fi 



dx dxdt 

lb 




r ^dF ^db ,dB. M 



Helmholtz, starting from the equation 

f Ydx + Gdy + B.dz = ff '""^' ds da, 

invest! gates^the most general form which F, G, H can have. He shows 
that we must write for - ^ of equation (11) the value 

-Ml^*^,"-''- • • • ("> 

where fc is an unknown constant. Hence 

v'F = -W+.(l-'O-0, . . . (W) 
and by comparing this with (13) we see that 

3=-Hk^ (16) 

dt 

' Glazebrook, Proc. Camh. PhU. Soc. vol. vi. pt. ii. See also J. J. Thomson, 
■' Report on Electrical Theories ' p. 133 oE this volume. 



ON OPTICAL THEORIES. 255 

If it be necessary that J should vanish, then Z; or — mnst be zero. 

dt 
According to Helmholfcz, however, J is not necessarily zero, and the 
equation to determine it is — 

^&k|J=a^J (17) 

so that J, and therefore *, is propagated through the medium as a 
wave of normal disturbance with the velocity 



1 



«uK 



On Helmholtz's theory there may therefore be a normal wave in addition to 
the transverse wave. Helmholtz's theory becomes Maxwell's if we put 
* = 0, and then unless the value Z; = oo is admissible J = 0, and there 
is no normal wave. If Z; = there will still be no normal wave for its 
velocity will be infinite. 

When we consider the problem of double refraction, we can show that 
all the possible directions of vibration L, M, N corresponding to a given 
wave normal I, m, n are given by the equation — 

■ E (^' - ^' + M ('" -'^') + I ^^"- ^') = • • (IS) 

There are therefore, in general, an infinite number of such directions. 
If, however, we are to assume that there are only two, and those the two 
given by Fresnel's theory, we must have IL + wiM + nTS = 0. Thus 
Maxwell's solenoidal condition, 

^+'ll+f=Q .... (]9) 
ax dy dz ^ ' 

is a necessary and sufficient condition to give Fresnel's construction. 



Chapter III. — Dispersion, etc. 

According to the theory as left by Maxwell, waves of all lengths 
travel at the same rate. Dispersion does not come into consideration. 
This question has been dealt with by Willard Gibbs • and H. A. Lorentz.^ 

§ 1. According to Gibbs's views the displacements of which we are 
cognisant in the phenomena of light are the average displacements taken 
through a space which is small in comparison with the wave length, but 
contains many molecules of the body. The real displacement at each 
point of such an elementary space probably differs considerably from the 
average value, and a complete theory should take into account the two. 
This is done in Gibbs's paper- The average displacements being I, r), ^, 
the complete displacement is taken as ^ + ^', &c. I', r,', ^' are denoted' as 
the irregular parts of the displacements. It is shown that i\ r]', C are 
linear functions of ^, 77, i; ; they are therefore of the same period, and the 
phase of the irregular displacement throughout the element Dv is the 

' J. W. Gibbs, American Journal of Science, vol. xxii. April, 1882. 
' H. A. Lorentz, Wied. Ann. t. ix.; Schlomilch. ZeiUcUrift, t. xxiii. 



256 EEPOET — 1885. 

same as that of tlie regular or average displacement, but the relations 
between ^, ??, ^ and H , r\' , C change rapidly as we pass from point to point of 
the element. 

The velocity of wave propagation is found by equating the maximum 
potential and kinetic energies of the medium. It is shown that the 
equations lead to Fresnel's consti-uction in the case of a crystal if the 
solenoidal condition be assumed, while the relation between f.i the refractive 
index and \ the wave length is given by 

1 _ H 2w,H.' 

y^--2-Kk'^ x^ .... (^u> 

H, l\ and H' being constants. The objection which Briot made to 
Cauchy's theory of dispersion may be made to this. We should expect 
dispersion in a vacuum as well as in ordinary transparent media. 

The properties of circularly polarising media are discussed in a second 
paper,' in which I', r/', ^' are treated as linear functions of s, jy, ^ and their 
differential co-efficients ; and in a third paper the fundamental equations are 
re-established in rather a more general form than that given by Maxwell. 

The generality is gained partly by dealing with the average values of 
the various quantities, and partly by supposing that the relation between 
the E.M.F. and displacement is given by 

[E] = [tj] + >// [U] : . . . (21) 

^ and </' being two arbitrary functions, and [ ] indicating that the average 
value is taken. In the simple theory ^ is a constant, and equal to 47r/K, 
and -^ zero, and this will not give dispersion. 

There seems, however, to be no reason — as has been pointed out by 
Professor Fitzgerald — against applying to the oscillations of the electro- 
magnetic field the methods and reasoning developed in the third part of 
this report. Almost the whole of the woi'k can be translated into the 
lano-uage of the electro-magnetic theory at once. Periodic electric dis- 
placement in the ether will produce periodic electric displacement in the 
matter, and the relations between the two will depend on the ratio of the 
period of the ether vibrations to the possible free periods of the electric 
oscillations in the matter molecules ; and it is not difiicult to see how the 
action between the two might depend on the relative electrical displace- 
ments and their differential coefficionts. 

§ 2. MaxwelP has given a theory of the magnetic rotation of the plane 
of polarisation on this theory. He assumes (1) that the effect of mag- 
netic force is to set up molecular vortices in the medium ; (2) that the 
components of the magnetic force obey the same law as the components 
of the strength of a vortex in hydrodynamics; and (3) that there arises 
in the value for the kinetic energy of the medium a term of the form 
2C(awi + /3w2 + ywj), w,, W2, ^3 being the components of the angular 
velocity, and a , /3, y of the magnetic force. 

For the case of waves travelling parallel to z the kinetic energy is 
shown to be 

T = i^>(^2 + f,^ + i-^) + cy(.) g - ig) . . (22) 

' J. W. Gibbs, American Journal of Science, vol. xxiii. June, 1882. 
« Maxwell, Electricity and Magnetism, vol. ii. p. 40. 



ON OPTICAL THEOKIES. 257 

and tlie equations of motion, 

From this it follows that the rotation per unit length is 

fl = „„,;l(i_x|) .... (24) 

where i is the index of refraction, and this formula agrees well with 
experiment. 

It should be noticed that in obtaining this formula Maxwell deals 
with the displacements of an ordinary medium ; the forces assnnied are 
those arising from the elastic reactions of this medium, the vortex motion 
in which is connected with the magnetic force. The displacements are 
not treated as identical with the electric displacements, nor is any indi- 
cation given of the connection between the two. 

§ 3. Fitzgerald, in the paper already mentioned, applies the theory to 
the case of reflexion from a magnetic medium. He finds that when 
plane polarised light is reflected directly from such a medium, the 
reflected light is slightly elliptically polarised. This is not in accordance 
with Kerr's experimental result, but Fitzgerald treats the iron as a trans- 
parent, or nearly transparent, substance with a real refractive index. 

§ 4. It was shown by E. H. Hall that when a current passes across 
a conductor in a magnetic field an electromotive force is produced whose 
strength is proportional to the product of the current and the strength of 
the field, and whose direction is at right angles to the plane containing 
the current and the field. 

By introducing into the equations for the electromotive force terms 
expressing this, so that they become 

^=-%-^-^{yg-fth) .... (25) 

at p 



etc., Prof. Rowland ' has calculated the magnetic rotation of the vectors 
F, G, H, and, on the assumption that a similar efiect will be produced 
in a dielectric, arrives at the same formula as that given by Maxwell. 

§ 5. The main difBculty of the theory, and the one which stands most in 
the way of its general acceptance, is the diSiculty of forming a clear phy- 
sical idea of what electric displacement is, and various analogies have been 
suggested with a view to rendering the difficulty less serious. One of these, 
due to Helmholtz,^ is developed in a paper on the molecular vortex theory 
of electro-magnetic action.^ It is shown there that, if the components of 
the magnetic force be identified with the molecular rotations in a con- 
tinuous medium in which the displacements are s, v, C, then the compo- 
nents of the electro-kinetic momentum are equal to J^^l, etc. ; and the 
equations of the electrical field in a conductor would imply that the 
medium in the conductor has the properties of a viscous fluid, while in a 
dielectric, so far as the motion to which the undulatory effects are due is 

' Eowland, Phil. Mag. April, 1881. 

- Helmholtz, Crelle Journal, t. Ixxii. 

^ Glazebrook, Phil. Mag. June, 1881. 
1885. a 



258 KEPOET — 1885. 

concerned, its properties are those of an elastic solid in which the elec- 
trical displacement / is given by 

^'/=-v^'+i(|4;40 . . . w 

The objection that it is impossible to maintain a continuous molecular 
rotation in an elastic solid may be made to this analogy. It seems, how- 
ever, possible that, as suggested by Professor Stokes when considering 
the problem of aberration, the ether may behave as a perfect fluid for all 
motions involving more than a very small relative displacement of its 
parts, while for such small displacements as are contemplated in the 
theory of light it has, in a dielectric, an appreciable rigidity. In a con- 
ductor the effects of this rigidity, if it exist, are masked by the more 
powerful effects of the viscosity. The fluid is no longer perfect. 

Chapter IV. — Rowland's Theory of the Peopaqation of Plane Waves. 

§ 1. The propagation of waves of electro-magnetic disturbance from 
a given source has been recently very fully considered by Professor 
Rowland,' and we proceed to give some account of his paper. 

Rowland considers very generally the solution of the equations — 

^=V2v2F, (27) 

etc., and allied equations given by the system 

F. + , ='^'--^' .... (28) 
so that F, G, H satisfy the solenoidal condition. He puts 

^_(,„+i) being a spherical harmonic, and C„ a function of p. 
He finds 

^^+2(a-i6)^?a.-JiOM:l)c,.=0 
dfj^ dp p^ 

whence 

f nn+1 n{n'^-l'') (n+2) 
C„-Co|l-^-^ +-^^5 ^" + - • 

where c = a — ib. 

He then takes, as a special solution, 

etc., and treats the case of symmetry round the axis of x, for which 

^ _ (- i)"Q.- i 

p"n! 

Q„_, being a zonal harmonic with the axis of x for axis. 

' Rowland, American Joxi/rnal of Mathematics ; Phil. Mag, June, 1884:. 



• 


(29) 


•} 


(30) 


. 


(31) 


• 


(32) 



ON OPTICAL THEOEIES. 259 

Let be tlie angle between this direction and that to the point at which 
the disturbance is required, p the distance to the point, and a the angle 
between the plane xOp and some fixed plane. 

Let 0', 9" denote disturbances perpendicular to the radius vector in 
the plane xOp, 

P' P" along the radius vector, and 

N' N" normal to the wave plane xOp. 

Then it follows that if we have small electric displacements X'e~'*'^~^'" 
parallel to x throughout the small sphere (fTrR' = dv), that 

e' = - 2^0+^2 gX' ^.^ Q^_ a^-vn^,, \ 
L/Q b-p 

P'= ^3!^'cos0e-'^O'-V'>(Zi; | ' 

Co 4Tp2 ) 

N' = 0" = P" = 
j^„^3&^X^sin0C,^_,,,,_v„^ 1 .... (34) 

0, = 0.(1-^1) 

3i 3^^• • • ■ (35) 



where 



C,= 



- ^° G - 4~by) 



This agrees with the results given by Stokes and Lord Rayleigh, already 
quoted,' N" being proportional to the rotation. The effect of a general 
arbitrary electric and magnetic displacement is then found. 

In considering the optical problem it is pointed out that electric 
displacement is always accompanied by magnetic, and that the effects of 
the two must be considered, and according to the views of Professor 
Rowland the two must be considered independently. From the relation 
between the electrostatic and electromagnetic energy, it follows that if 
there be an electric displacement X'e*^' there will be a magnetic Y"e'"'' 
where 

Y" = ^X'. 

The electric displacement at any other point of space is found and 
expressed as below. Let the origin be the point at which X', Y" act ; the 
axis of z the normal to the plane of X'aY" ; p the direction in which the 
effect — at a point A — is required ; the angle 2OA = d, and the angle between 
zOA and zOx = ^ ; and let P', 0', 4>' be the displacements along OA, and 
normal to 6 and f. 

Then 

e' ='!pT cos <p [a + COS d)(l -i] - e^l e-':^o.-vo ^ 

8'^P ^[_^ -T ^\^ j^; ^2^2]^^ [-(36) 

P'= ^4^8in0cos9.ri_lV'^^-v« 

47rp2 r ^ ^^j 

' See p. 201. 

82 



260 EEPOET — 1885. 

And we can show that in the value of 6' it is the 1 in (1 + cos 0) which 
comes from the assumed magnetic disturbance, while in <S>' it is the cos d 
in the same term. 

The magnetic disturbance produces no effect in the value of P' . Neglect- 
ing the magnetic disturbance we arrive at Stokes's result for the effect of 
a disturbance X'e''^'* on the medium, which is used by Rayleigh in the 
paper on the blue of the sky. 

Now we may note that the result of the experiments on scattered 
light seems to disprove this hypothesis of Rowland's as to the necessity of 
considering the two disturbances, for according to him the intensity is the 
same at all points in the plane xy at the same distance from O. This is 
not true ; the intensity varies as sin^a if a is the angular distance of the 
point from the axis of x. Again, it is true, of course, that the magnetic 
disturbance accompanies the electric, but it accompanies itas a consequence. 
If we produce, by some impressed force, a varialale electric displacement 
at a point in the medium, and calculate the effect due to this, we have 
done all that is necessary. There will, it is true, be magnetic displace- 
ment, but it can be calculated from the electric. 

Rowland's results do not apply to the case of a wave being propa- 
gated through an aperture, for in this case we have no right to assume 
that the disturbance produced by an element is symmetrical round 
the direction of vibration . We have not a single particle or an indefi- 
nitely small sphere vibrating and sending out its effects in spherical 
waves ; we have a state of motion coming in from behind the aperture, 
and being continually propagated across it at a given point P and at 
time to, we must consider the circumstances at any point O of the 
aperture at a time t^ such that OP = &(i — fo)- For these will be the 
initial circumstances so far as we are concerned ; and at this time t^, 
has an initial velocity and an initial displacement, Both these require to 
be considered in dealing with the question, and we have to adopt Stokes's' 
method of solution, and we again arrive at his theorems with regard to 
the relation between the direction of vibration and the direction of 
diffraction. 

§ 2. The electro-magnetic theory, if we accept its fundamental hypo- 
theses, is thus seen to be capable of explaining in a fairly satisfactory manner 
most of the known phenomena of optics. The great difficulty is, as we 
have said, to account for the properties which the medium must have in 
order to sustain electrical stresses. These consist in an electrostatic field 
of a hydrostatic pressure KR^/Stt, combined with a tension KR^/47r 
along the lines of force ; R being the resultant electrical force, and K 
the inductive capacity. There will therefore be a difference of pressure 
in different directions in the ether. 

Combined with this difficulty there is another of a similar kind, that 
of realising mechanically what electric displacement is, of forming for 
oneself a physical idea of a change of structure in some medium of 
unknown properties which shall obey the laws implied by the various 
equations satisfied by the components of electrical displacement. 

Optical effects are certainly due to changes, periodic in space and I 
time, of some properties of a medium which we call the ether. Electro- 
magnetic effects are also due to variations in properties — it may be the 
same as those which give rise to light — of the same ether. When the 

' On this point reference has already been made, see p. 206. 



ON OPTICAL THEOEIES. 261 

electro-magnetic effects become rapidly periodic they travel -with the 
velocity of light, and the direction to which the change of property is 
related is in the wave front, at least for isotropic media. 

The rigidity or quasi-rigidity through which the medium has the 
power of propagating these transverse waves of small displacement may 
be given to it through other motions which are going on independently 
of the light. The free passage of the planets through space proves that 
it can have little if any viscosity or rigidity, though, according to the 
views of Professor Stokes, while behaving as a perfect fluid for all 
appreciable motions, it might conceivably be rigid for the very small 
displacements in a light-wave. Taking Sir W. Thomson's estimate of 
the density of the ether as about 10"^- grammes per cubic centimetre, the 
rigidity required for the propagation of light would be about 10""^ The 
rigidity of glass is about 2-5 X 10". While it might, then, be conceivable 
that the ether should have this very small rigidity and yet ofier no 
appreciable resistance to the earth's motion, it is difficult to reconcile 
this with its power of standing electric stress, and we are forced to con- 
clude that the change implied in electric displacement is much more 
than a mechanical displacement of the molecules of a perfect fluid. A 
qnasi-rigidity might be conferred on the fluid by filling it with vortices, 
and it might thus become capable of conveying transverse waves and of 
standing electric stress. Electric and magnetic polarisation would then 
consist in definite arrangements of the vortex rings or filaments. Changes 
in these arrangements, or in some of the properties connected with them, 
would constitute electric and magnetic displacements, and possibly also 
h'ght. 

We should then have a complete electro-magnetic theory of optics, or 
rather a complete theory of the ether embracing electro-magnetism and 
optics, but towards this theory our present knowledge has made only a 
small advance. 



Report of the Committee, consisting of Professors Ramsay, Tilden, 
Marshall, and W. L. GtGODwin (Secretary), appointed for the 
purpose of investigating certain Physical Constants of Solution, 
especially the Expansion of Saline Sohdions. 

TocR Committee have to report as follows : 

They have obtained apparatus for determining the rates of expansion 
of saline solutions fi-om -20° C. to -f60° C. 

They have devised experiments for determining the distribution of a 
weighed quantity of water between molecular weights of two salts, the 
three substances being placed in separate vessels in the same enclosed 
space kept at a constant temperature. 

But further progress in either of these directions was interrupted by 
the continued illness of one of the Committee. 

Your Committee respectfully ask for reappointment. 



262 EEPORT— 1885. 



Third Report of the Committee, consisting 0/ Professors Williamson, 
Dewae, Frankland, Crum Brown, Odling, and Armstrong, 
Drs. Hugo Muller, F. E. Japp, and H. Forster Morley, and 
Messrs. A. Gr. Vernon Harcourt, C. E. G-roves, J. Millar 
Thomson, H. B. Dixon (Secretary), and V. H. Veley, reap- 
pointed for the purpose of dratuing up a statement of the 
varieties of Chemical Names ^vhich have come into use, for 
indicating the causes tvhich have led to their adoption, and 
for considering what can he done to bring about some conver- 
gence of the views on Cheriiical Nomenclature obtaining among 
English and foreign chem,ists. 

An account of tlie authorship of some of the various systems of nomen- 
clature which have been devised for the purpose of distinguishing between 
compounds formed by the union of the same elements in different propor- 
tions, has been given in the ' Historical Notes ' prefixed to the Second 
Report of this Committee. Among these systems the use of the termina- 
tions oMs and ic, to denote respectively lower or higher degrees of saturation 
of one element or group with another element or group, is perhaps that 
which has met with the widest acceptance. This system further directs 
that when electro-negative groups, the names of which end in ous and ic, 
unite with electro-positive groups to form salts, these terminations are to 
be changed into ite and ate respectively. 

Before proceeding to discuss the practical application of this system, 
it may bo well to point out, as a minor etymological detail, that the literal 
meaning of the terminations ous and ic has altered since they were first 
employed. Thus ous (Latin osus) ought to denote, on the part of the 
compound, richness in that element to the name of which the termination 
is attached. For example, cujirous (cuprosus) means ' rich in copper ' : 
cuprous oxide is primarily an oxide which is richer in copper than cupric 
oxide, and only by implication an oxide which is poorer in oxygen. This 
implied signification is, however, that in which the name cuprous oxide 
is nowadays employed. A curious result of this change of literal meaning 
is to be found in the use of the prefix hypo to denote a still lower degree of 
saturation than that expressed by ous. Thus the name hyponitrous acid 
is taken to denote an acid containing still less oxygen than nitrous acid ; 
whereas hyponitrous really means ' less rich in nitrogen,' which is the vdty 
opposite. Had the etymology been logically carried out, the prefix ought 
to have been hyper. A similar confusion of ideas is displayed in the use 
of the prefixes hyper and per at the other end of the scale ; in place of 
these, hypo ought to have been employed. Ferchromic acid does not, as 
its name literally taken signifies, contain more chromium than chromic 
acid : it contains less, and ought consequently to have been termed 
/typo-chromic acid. 

It need hardly be said that it would be ill-advised to attempt to 
change a system so firmly established as that involved in the present 
use of these prefixes hypo and hypier ; and in the above remarks on 
the etymology of the subject, nothing of the kind is intended. No 
ambiguity can arise from the use of terms about the meaning of which 
everyone is agreed, and their mere etymological accuracy is, in view of 
this all-important consideration, of secondary importance. 



ON CHEMICAL NOMENCLATUBE. 



263 



The following list will show the application of the ic and ous nomen- 
ilature to salts and salifiable oxides : — 

I. List of Salts where Two or more Series of Compounds are formed.^ 



Name denoting metallic 


Formula of corre- 


Name denoting metallic 


Formula of corre- 


radical of salt 


sponding oxide 


radical of salt 


sponding oxide 


Cuprous 


Cu.O 


Chromous 


CrO 


Cupric 


Cub 


Chromic 


Cr„03 


Mercurous 


Hg,0 


Uranous 


u6„ 


Mercuric 


HgO 


Uranic ( tJranylic) 


UO3" 


Aureus 


Au„0 


Manganous 


MnO 


Auric 


Au„03 


Manganic 


Mn,03 


Thallous 


Tlo'O 


Ferrous 


Feb 


Thallic 


TLO3 


Ferric 


Fe,03 


Stannous 


Snb 


Cobaltous 


CoO 


Stannic 


SnO„ 


Cobaltic 


Co„03 


Cerous 


CeoO'a 


Platinous 


PtO 


Ceric 


Ceb„ 


Platinic 


PtO^ 



Names corresponding with ijlatinous and platinic would be applied to 
the corresponding oxides and salts of the other metals of the platinum 
gi'oup — distinguishing, however, the other oxides and salts of this group 
by numeral or other designations. 

The designations given in this Table to the various higher and 
lower series of salts and salifiable oxides have been employed with almost 
complete uniformity by all chemists who have adopted this system of 
nomenclature. 

As a metal rarely — if ever — forms more than two salifiable oxides, the 
ous and ic terminations generally suffice for purposes of distinction so far 
as the salts of metals are concerned. 

The practice of further employing these terminations in the case of 
acid-forming oxides does not lead to confusion, since these oxides are 



distinguished by the name anhydride (or acid). 
CrO Cr^Og 



Chromous oxide. 



Thus we have 

Cr03 

Chromic oxide. Chromic anhydride 

(Chromic acid.) 

Indifferent oxides have frequently been classified and named by 
regarding them as compounds of salifiable, with acid-forming oxides, 
CrjO^ being termed chromic chromate. For stages lower than ous, the 
prefixes hi/po and sub are employed. Custom appears to have restricted 
hypo chiefly to acids and to acid-forming oxides, suh to salifiable and to 
indifferent oxides. 

With regard to the termination o^is, the minor question arises, how 
far this termination ought to be written in the forms ious and ecus. 
The answer is : as seldom as possible. ' Cupreous ' has generally given 
way to ' cuprous ' ; no one writes ' chromious ' (although the name of 
the metal is ' chromium ') ; and there is no reason why such names as 
' ruthenious ' and ' iridious ' should not equally be shorn of their super- 
fluous penultimate syllable. 

A further question, concerning which considerable difference of opinion 
has prevailed, is whether any ous or ic terminations ought to be 
employed in the names of salts of which only one class is known — thus 
magnesic sulphate instead of magnesium sulphate. There is something to 

' In this list the term ' salt ' is taken to include ' haloid salts,' but to exclude the 
halogen compounds of those elements whose oxides do not yield oxy-salts with acids, 



264 . EEPORT — 1885. 

be said here for both systems ; and, as the diversity of practice does not lead 
to confusion, and conseqnently does but little harm (beyond in each case 
offending the ears of those accustomed to the opposite system), the ques- 
tion need not be regarded as a vital one. Objections which have been 
urged against the use of any termination in such cases are that chemists 
have not always been able to agree as to which termination is to be used 
in a given case, and that, apart fi"om this, the practice causes beginners 
erroneously to surmise the existence of a second series of salts. The 
objection on the other side is that the omission of the terminal ' ic ' breaks 
the uniformity of the system and leads beginners to suppose that barium 
sulphate, for instance, has a different constitution from cupric sulphate. 
In the case of carbon compounds, on the other hand, there is a distinct 
advantage in aflSxing ic to the names of the positive radicals in ethereal 
salts. A neglect of this precaution leads to ambiguity — at all events in 
the spolcen name. Thus, though tliere is no ambiguity in the name etlujl 
loTienijlacetate when written, yet the ear cannot distinguish between it and 
etlujlpTienyl acetate. This ambiguity is obviated by the use of the termi- 
nation ic : thus, eilnjlic plienylacetate and efJiylphenylic acetate. 

In the use of the terminations ous and ic to distinguish different series 
of acids and acid-forming oxides, the practice of chemists has also been 
very uniform. Indeed, with the exception of one or two isolated cases 
almost perfect unanimity has prevailed. 

To sum up, the ous and ic terminations when employed for purposes 
of distinction in cases where two series of oxides, acids, salts, &c., are 
known, have been almost free from ambiguity, and for this reason 
deserve to be retained. On the other hand, in cases where only one series 
is known, those chemists who have employed one or other of these 
terminations have occasionally differed as to which ought to be used : 
the difficulty may be solved, as it has been done by some chemists, by 
avoiding the use of any termination in such cases. 

In complex cases where the above modes of naming prove inadequate, 
recourse may be had to numeral designations. These appear especially 
admissible in cases where an oxide occurs which is intermediate between 
the ous and ic stage, and at the same time cannot be classed as a com- 
pound of oxides already classified and named. 

In applying numeral designations, it is most important to select only 
such as are free from hypothesis and which afford correct information. 
In this respect, chemists appear of late years not to have been sufficiently 
careful. As an example, arsenious oxide may be quoted ; this compound 
is frequently termed 'arsenic trioxide,' the formula being written AsgOj, 
and it is tacitly assumed that the molecule contains three oxygen atoms. 
There are three objections to this name: — (1) That, assuming the formula 
on which it is based to be correct, it affords no information as to the 
number of arsenic atoms associated with the three oxygen atoms ; (2) 
that it involves the assumption that arsenious oxide does not vary in 
molecular weight, whatever its physical state ; and (3) that the formula 
of gaseous arsenious oxide is AS4O6. 

In employing numeral designations to indicate molecular composi- 
tion in cases where this is established, it is therefore important to express 
the number of atoms of each constituent element, as dicarhon hexachloride, 
C2 Clg. But in the case of solid and liquid bodies of which the molecular 
weight is either unknown or may vary with temperature, the name 
should indicate merely the relative proportions in which the constituents 
are associated ; or, more explicitly, the name should indicate the proper- 



ON CHEMICAL NOMENCLATURE. 265 

tion of the radical associated with what may be termed the characteristic 
element of the compound. No difficulty occurs in the case of the chlorides, 
or analogous compounds with the monad elements generally, these being 
termed mono-, di-, tri-, tetra-, penta-, or hexa-chloride, &c., according as 
combination is in the proportion of 1, 2, 3, 4, 5, or 6 atoms of chlorine to 
1 atom of the characteristic element. The application of this system 
would involve the use of the names tin dichloride and iron trichloride 
(not sesqui-chloride) for stannous and ferric chlorides respectively, names 
which accurately express the relative proportions of chlorine to metal in 
these compounds without any hypothesis as to their molecular composition 
— a composition, which in the case of the former compound, at all events, 
certainly depends on temperature. It will, however, involve a slight depar- 
ture from the existing practice when applied to oxides, sulphides, and other 
compounds of polyad elements ; thus oxides of the type (R2)"0 would 
be termed hemi-o-K.ides, since they consist of the characteristic element 
and oxygen in the proportion of one atom of the former to half an atom. 
of the latter. Oxides of the type (R2)"03 would be termed sesqui- 
oxides, since the characteristic element and oxygen are present in the 
proportion of one of the former to one and a half of the latter. Oxides of 
the type R2 O5 would be termed sesterti-oxides, as they contain oxygen 
and the characteristic element in the proportion of two and a half 
atoms of the former to one of the latter. Oxides of the types RO, 
RO2, RO3, and RO4, would be termed respectively mono-, di-, tri-, and 
<e<r-oxides. 

Acid Salts. 
There are two distinct classes of salts to which this name has been 
given : — 

1. Salts with two or more metals, one of the metals being hydrogen. 

2. Salts formed from these by the removal of water. 

Until comparatively lately, no attempt was made to give distinctive 
names to these two classes, except that sometimes the words hydratic and 
anhydrous were used to distinguish them. The distinctive names — 
pyrophosphate, metaphosphate — which Graham gave to the two sets of 
anhydrous acid phosphates were founded on the supposition that the 
phosphoric acid (PO5) existed in them in two modifications, different 
from the acid of the ordinary phosphates. 

The nomenclature used by nearly all chemists from the beginning of 
this century until about 1860 is illustrated on tables 3-6. Acid salts in 
which for the same quantity of base there is 2, 3, . . . &c. times as much 

acid as there is in the normal salt are called hi ate, ter ate, &c. (in 

German, doppelt (or zweifach) saures Salz, dreiiach saures Salz, 

&c.) In English and French the Latin adverbial numerals his or hi, ter, 
&c. seem always to have been used until about twenty years ago, when 
Greek adverbial numerals were introduced for the anhydrous acid salts. 
Watts's Dictionary and Naquet are the first English and French 
authorities in which we have observed this change. 

Basic Salts. 

There are two distinct classes of salts to which this name has been 
given : — 

1. Salts with two or more salt radicals, one of the salt radicals being 
hydroxyl. 

2. Salts formed from these by the removal of water. 



266 KEPOET— 1885. 

These were not distinguished by name until quite recently, and are 
still very often confused. 

The nomenclature in general use is illustrated on tables 8-12. 

Basic salts of oxygen acids in which for the same quantity of base there 
is ^, ^, &c. as much acid as there is in the normal salt are called 

di ate, tri (or tris) ate, &c. (in German, halb saures Salz, 

drittel saures Salz, &c.) 

Basic salts of oxygen acid were also named by the proportion of base 
to acid, the proportion in the normal salt being taken as unity — bibasic, 
terbasic, &c. salts (in German, zweifach, dreifach, etc. basische Salze). 
Thus ^rt'snitrate (drittel saures salpetersaures Salz) is the same as terhasic 
nitrate (dreifach basisches salpetersaures Salz), Latin adverbial numerals 
being used for multiples, and Greek adverbial numerals for submultiples. 

The compounds of basic oxides with haloid salts (corresponding to 
the basic salts of the oxygen acids) are variously named ; thus, oxy- 
chloride, bisoxychloride, basic chloride, bibasic chloride. The numerals 
here refer not to the number of atoms of oxygen and halogen, but to the 
proportion of metal combined with oxygen and halogen respectively 
(or perhaps more correctly to the proportion of equivalents of oxygen and 
halogen) ; thus 2PbO.PbC]2 is bisoxychloride, or bibasic chloride. It is 
to be noted that corresponding basic haloid and oxygen salts have not the 
same numeral ; as — 

PbO.PbClo is basic chloride (einfach basisches Chlorid). 

PbO.Pb(N03)9 is bibasic nitrate (zweifach basisches Salz), because 
it is 2PbO.]Sr20g. 

2PbO.PbCl2 is bibasic chloride (zweifach basisches Chlorid). 

2PbO.Pb(N03)o is terbasic nitrate (dreifach basisches Salz), because 
it is SPbO.NgOs- 

Sulphur Salts. — Table 14. 

These have sometimes, especially in German, been named as double 
sulphides, but usually, in Latin, English, French, and recently also in 
German, follow the names of the corresponding oxygen salts. 

Sulphur Basic Salts. — Table 1 3. 
Compounds of normal salts with sulphides of the metal. These were 
discovered by H. Rose, and called by Berzelius sulphur basic (schwefel 
basisch), as corresponding to the compounds of normal salts with the basic 
oxide. This nomenclature has not been generally adopted, and, as will be 
seen from the table, there is little uniformity in naming these substances. 

Double Salts. 

With very few exceptions, these may be classified in two sets. 
1. With a common salt radical. 2. With a common metal. 1. With a 
common salt radical. Here again there are two kinds, (a) Salts of 
polybasic acids. (6) Compounds of two haloid salts, or of a haloid salt, 
with a compound of a halogen and a non- metallic element. 

(a) These are named consistently with the names of the simple salts j 
as phosphate of magnesia and ammonia, phosphorsaure ammoniak- 
magnesia, magnesium ammonium orthophosphate, ammonic magnesio 
phosphate, or, with what may perhaps be called an adverbial modification 
of the first adjective, ammonio-magnesic phosphate. 

(h) Of these we may take as examples 2KF, Sir4 ; 2KC1, PtCl4 ; 
2KCN, Pt(CN)2; KF, BF3 ; KCl, AuClg ; 4KCN, Fe(CN)2 ; 3(KCN), 
Fe(CN)3. See Tables 15, 16, 17. 



ON CHEMICAL NOMENCLATURE. 



267 



These have been named on three different principles : — 

(a) As double fluorides, chlorides, etc. ; for instance, fluoride of silicon 
and potassium, fluorkieselkalium. T!^T 

(fi) As compounds of the positive metal with a compound salt radi- 
cal ; for instance, ferrocyanide of potassium, silicofluoride of potassium, 
kieselflu orkalium . 

(7) As analogues of oxygen salts ; for instance, fluosilicate of 
potassium, potassium fluosilicate, potassium chlorplatinate, chloraurate, 
cyanaurate. 

The third system seems only to be used when there is really a corre- 
sponding: oxygen compound. 

2. With a common metal. As a well-known substance mentioned by 
most systematic writers, emerald green has been selected — table 18. 
It will be seen that where a name is given, it is either acetate and 
arsenite, or a combined name, acetoarsenite, or arsenigessigsaures Salz. 

List of Authorities referred to hy their nurribers in, thefolloioing tables. 



No. 



1 

2 
3 
4 
5 
6 
7 

8 
9 
10 
11 
12 
13 
14 

15 
16 

17 
18 
19 



Author 



Thomson . . 
Thomson . . 
Thomson . . 
Brande . . . 
Thomson . . 
Brande . . . 
Ongren (Table to 

Berzelius) 
Brande .... 
Graham . . . 
Gmelin .... 
Liebig (Geiger) . 
Mitscherlich . 
Handworterbuch 
Kopp's Geschichte 

(vol. iv.) 

Kane 

Graham . . . . 

Eegnault . . . . 

Fownes 

Otto 



Edition 


Date 


No. 
20 


II. 


1804 


IV. 


1810 


21 


V. 


1817 


22 


I. 


1819 


23 


vir. 


1831 




IV. 


1837 


24 


IV. 


1838 


25 
26 


V. 


1841 


27 


I. 


1842 


28 


IV. 


1843-4 


29 


V. 


1843 


30 


IV. 


1844 




I. & II. 


1848-64 


31 


— 


1847 


32 


II. 


1849 


33 


II. 


18.50 & 
1858 


34 


III. 


1851 


35 


V. 


1854 


36 


III. 


1855-60 





Author 



Miller 

Eegnault . . . . 
Rose (French) . . 
Watts's Dictionary 

and Supplements 
Naquet .... 
Eose (Finkener) 
Fownes . . . 
Williamson . . 
Wurtz's Dictionary 
Bloxam .... 
Eegnault Strecker- 

Wislicenus 
Kolbe, Kurzes Lebr- 

buch 

Fownes 

Miller 

Eoscoe and Schor- 

lemmer 
Frankland and Japp 
Kolbe (Humpidge). 



Edition 


Date 


I. 


1856 


V. 


1859 


— 


1862 


— 


1863-81 


II. 


1867 


VI. 


1867-71 


X. 


1868 


II. 


1868 


— 


1869-76 


II. 


1872 


IX. 


1877 


— 


1877-8 


XII. 


1877 


VI. 


1878 


— 


1878-81 


_ 


1884 


" 


1884 



1. Muriat of lime. 

2. Muriate of lime. 

3. Chloride of calcium (also muriate of 

lime). 

4. Chloride of calcium. 

5. Chloride of calcium. 

6. Chloride of calcium (cal + C). 

7. Chloretiim calcicum (CaCl). 

8. Chloride of calcium or muriate of 

lime (Cal+C). 

9. Chloride of calcium (CaCl). 

10. Chlorcalcium (CaCl). 

11. Chlorcalcium (calcium chloratum) 

(CaCl,). 

12. Chlorcalcium (CaCl). 



13. Calciumchlorid, chlorcalcium (Salz- 

saurer Kalk) (CaCi), 1859. 

14. Chlorcalcium. 

15. Chloride of calcium (CaCl+6Aq). 

16. Chloride of calcium (CaCl). 

17. Cblorure de calcium (CaCl). 

18. Chloride of calcium (CaCl). 

19. Chlorcalcium (CaCl). 
Chloride of calcium. 
Chlorure de calcium (CaCl). 



20. 
21. 
22. 
23. 



24. 
25. 



Chloride of calcium (CaCL). 

S upp . C alciu m cliloride . 
Chlorure de calcium. 
Chlorcalcium. 



2nd 



268 



REPORT — 1885. 



26. Calcium chloride (CaClj). 

27. Calcic chloride (CljCa). 

28. Chlorure de calcium. 

29. Chloride of calcium (CaClj). 

30. Chlorcalcium (CaCL). 

31. Chlorcalcium (Ca"Cl2). 

32. Calcium chloride (CaCl,). 



1. Sulphat of soda. 

2. Sulphate of soda. 

3. Sulphate of soda. 

4. Sulphate of soda. 

5. Sulphate of soda. 

6. Sulphate of soda (S + .s')- 

7. Sulphas natricus (Na S) 

8. — 

9. Sulphate of soda (NaO,S03+ lOHO). 

10. Einfach schwefelsaures Natron. 

11. Schwefelsaures Natron (natrum 

sulphuricum) (NaO,S03,10Aq). 

12. Schwefelsaures Natron (NaS + lOAq). 

13. Schwefelsaures Natron, neutrales, 

1859. 

14. Schwef(;lsaures Natron. 

15. Sulphate of soda (NaO.SOa + lOAq). 

16. Sulphate of soda (NaO.SOa). 

17. Sulfate de soude (NaO,S03). 

18. Sulphate of soda (NaO.SOa). 

19. Schwefelsaures Natron (NaOjSOj). 

20. Sulphate of soda (NaO.SO,). 

21. Sulfate de soude (NaO.SOj). 



33. Calcic chloride (or chloride of cal- 

cium) (CaCU). 

34. Calcium chloride (chloride of cal- 

cium) (CaCl.,). 

35. Calcic chloride (CaCU). 

36. Calcium chloride (CaClj). 



n. 



22. — 

23. Normal or neutral sulphate of 

sodium. 2nd Supp. sodium sul- 
phate (Na.SOJ. 

24. Sulfate neutre de soude. 

25. Schwefelsaures Natron. 

26. Sodium sidphate (SO^Naj) 

27. Sodic sulphate (Na.SOJ. 

28. Sulfate neutre de sodium. 

29. Sulphate of soda (NajO.SOj). 

30. Neutrales schwefelsaures Natrium, 

Oder Dinatriumsulfat (Na^SO^, 
lOH^O). 

31. Schwefelsaures Natron, neutrales 

32. Sodium sulphate. 

33. Sodic sulphate, or sulphate of 

sodium (Na^SOj). 

34. Normal sodium sulphate (also sul- 1 

phate of soda). 

35. Sodic sulphate (SOjNaOj). 

36. Sodium sulphate. 



III. 



1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 

10. 
11. 

12. 



13. 

14. 
15. 

16. 

17. 



Supersulphate of soda. 
Bisulphate of soda. 
Bisulphate of soda. 
Bisulphate of soda. 
Bisulphate of soda. 

Bisulphate of soda. 
Bisulphate of soda 
0,S0,). 



(H0,S03 + Na 



Saures (od. doppelt) schwefelsaures 
Natron (NaO,2S03 + Aq). 

Schwefelsaures Natron und schwefel- 
saures Wasser, zweifach schwefel- 
saures Natron (NaS- + 3H = NaS + 

HS + 2H). 
Schwefelsaures Natron, zweifach 

saures, wasserhaltendes Salz 

(NaO,S03 + HO,S03). 
Saures schwefelsaures Natron. 
Bisulphate of soda (NaO,S03 + HO, 

SO3). 
Bisulphate of soda (HO.SOs + NaO, 

SO3). 
Bisulfatede soude (NaO.SO^-t- HO.SO' 
+ 2H0). 



18. Bisulphate of soda (NaO.SOa + HO, 

SO3 + 3H0). 

19. Zweifach schwefelsaures Natron, 

Wasserhaltiges (NaO,S03 + HO, 
SO3). 

20. Bisulphate of soda (NaO,HO,2SO,'). 

21. Bisulfate de soude (NaO.SO» + H0. 

S0» + 2H0). 

22. Bisulphate de soude. 

23. Hydro-monosodic sulphate (hy- 

drated bisulphate of soda) (NaH 
SO,). 

24. Bisulfate de soude. 

25. Saures schwefelsaures Natron. 

26. Sodium and hydrogen sulphate, or 

acid sodium sulphate (2S04NaH. 
3OH2, or SO,Na2.SO,H,.30H2). 

27. Hj'drosodic sulphate (NaHSOj). 

28. Sulfate acide de sodium (SO^NaH). 

29. Bisulphate of soda (Na20,H20,2S03). 

30. Mononatrium Sulfat, oder halbge- 

siittigtes saures schwefelsaures 
Natrium. 

31. Saures schwefelsaures Natron fONa 

S0„10H 

32. Sodium and hydrogen sulphate, 01* 

acid sodium sulphate (see 26). , 
S3. Hydric sodic sulphate (acid sul-j 



ON CHEMICAL NOMENCLATURE. 



269 



pliate of sodium or bisulphate of 
soda) (NaHSO^). 
34. Hydi-ogen sodium sulphate (NaH 
SOJ. 



35. Hydric sodic sulphate (SO^HoNao). 

36. Acidsodium sulphate S0„ f {qm ") 



IV. 



1. 

2. 
3. 

4. 
5. 
6. 

7. 
8. 

9. 

iio. 

11. 

I 12. 
I 13. 

' 14. 
15. 

16. 

17. 

18. 

19. 



See Table III. 



Anhydrous bisulphate of soda (S + 

2s')- 
Bisulphas iiatricus Na iS.^. 
Anhydrous bisulphate of soda (S 

+ 2s'). 

Zweifach schwefelsaures Natron 
(NaO, 2SO3). 

Saures (doppelt) schwefelsaures Na- 
tron, das wasserleere Salz. 

Schwefelsaures Natron, zweifach 
saures wasserfreies Salz. 

(Not specially named.) 

Anhydjous bisulphate (a true bisul- 
phate). 

Un veritable bisulphate (Na0.2S03). 

Anhydrous bisulphate of soda (NaO, 
2.SO3). 

Zweifach schwefelsaures Natron, 
wasserfreies Salz (NaO,2S03), 



20. 

21. 
22. 
23. 



24. 
25. 
26. 
27. 
28. 
29. 
30. 

31. 



32. 

33. 
34. 
35. 

36. 



Bisulphate of soda, the anhydrous 

salt. 
Un veritable bisulphate (Na0.2S0'). 

Anhydrosulphate of sodium or an- 
hydrous bisulphate of sodium 
(Na„S.,0. = Na„S0„S03 = Na„0, 
2SO3) 1875. 

Disulfate de sonde. 

Anhydro bisulphate (S0,Na„,S03). 
Sodic disulphate (NaoS^O,).' 
Anhydrosulfate. 

Neutrales Kalium Pyrosulfat. 

Dischwefelsaures Natron 

/^/SO,ONa\ 
\^ \,SO.,ONaj 

Pyrosulphate (NajSoO, or Na„SO,, 

SO3). 
Sodic pyrosulphate (Na^S^O,). 
Sodium disulphate (Na.SJO,). 
Sodic pyrosulphate (S^O^NaOo). 

Sodium disulphate (0{«ggNa^J 



V. 



1. 
2. 
3. 
4. 
5. 
6. 

7. 

8. 

9. 
10. 
11. 
12. 
13. 

14. 

15. 
16. 

17. 

18. 
19. 

20. 
21. 
22. 
23. 



(Alkaline chromats.) 

Chromate of potash [red colour]. 

Bichromate of ijotash. 

(Not distinguished from chromates.) 

Bichromate of potash. 

Bichi-omate of potassa (2Chr' + P). 

Bichromas kalicus (KCro). 
Bichromate of potassa (2Chr' + P). 
Bichromate of potash (KO,2Cr03). 
Not mentioned. 

>> >> 

Zweifach chromsaures Kali. 

Doppeltsaures od. rothes chrom- 
saures Kali (KO,2Cr03), 1859. 

Bichi-omate of potash (KO + 2Cr03). 
Bichromate of potash (KO,2Cr03), 

_ 1858. 
Bichromate de potasse. 
Bichromate of potassa (KO,2CrOg). 
Zweifach od. rothes chromsaures 

Kali (KaO,2Cr03). 
Bichromate of potash (KO,2Cr03). 
Bichromate de potasse. 

Acid chromate of potassium, di- 
chromate of potassium, or bi- 



chromate of potash (K„0.2Cr03 
- K2CrOj,Cr03), 1863. Potassium 
dichromate (K20.2Cr03), 1872. 

24. Dichromate de potasse. 

25. Saures chromsaures Kali. 

26. Potassium bichromate or anhydro- 

chromate (2Cr03,K.O, or CrO.K,, 
CrOg). 

27. Potassic dichromate (K„Cr,0,). 

28. Bichromate de potasse (K„0,2Cr03). 

29. Bichromate of potash (K„0,2Cr03). 

30. Kalium dichromat. 

31. (Neutrales) Dichromsaures Kali. 

/f. (CrO,OK\ 
\^ lCrO„OKj- 

32. Potassium bichromate or anhydro- 

chromate (2Cr03,KoO, or CrO.K,, 
Cr03). 

33. Potassic dichromate, pyrochromate, 

or anhydrochromate (K„0,2Cr03, 
or KXr^O,). 

34. Potassium dichromate, or bichromate 

of potash (KoCr^O,). 

' ' / (CrO^Ko N 

35. Dipotassic dichromate (JO ) 

\ (CrO„Ko / 

36. Potassium dichromate. 



270 



REPORT 1885. 



VI. 



1. — 

2. — 

3. — 
i. — 

5. — 

6. — 

7. — 

8. — 

9. Terchromate of potash (KO.SCrOj). 

10. — 

11. — 
12 
13 



14. 
15. 
16. 

17. 

18. 
19. 

20. 
21. 
22. 



Dreifach chromsaures Kali. 
Dreifach chromsaures Kali (KO, 
SCrO^). 



Terchromate of potash (KO.SCrOs) 

[1858]. 



Dreifach chromsaures Kali (KaO, 

SCrOj). 
Terchromate of potash (KO.SCrOj). 



23. 



24. 
25. 
26. 

27. 
28. 
29. 
30. 
31. 
32. 

33. 
34. 



Hyperacid chromate or trichro- l 
mate of potassium (K„0,3CrOs 
or K2Cr04.2Cr03 [1803], po- 
tassium trichromate (K20,3Cr03) 

[1872]. 



Potassium trichromate (3Cr03,K,0, 
or CrO^K„,2Cr03) 



Terchromate of potash (KjO.SCrOj), 
Kalium trichromat. 

Potassium trichromate (3Cr03,K,0, 

or CrO.,K„,2Cr03). 
Potassic trichromate (K„0,3Cr03). 
Potassium trichromate (K^CrjO,,,). 

'CrOaKo 



35. Dipotassic trichromate 




36. 



VII. 



1. 
2. 
3. 
4. 
5. 
6. 

7. 
8. 



10. 
11. 
12. 

13. 



14. 
15. 
16. 

17. 



18. 



Bichromate of chloride of potas- 
sium. 

Bichromate of chloride of potas- 
sium. 
Bichromate of chloride of potassium 
(KCl-(-2Cr03). 



Chromsaure und Chlorkalium (KGl -i- 2 

Cr). 
Zweifach chromsaure Chlorkalium, 
chlorchromsaure Kali (KGl,2Cr03 
Oder KO,Cr03.CrO„ei oder 3(K0. 
Cr03) + (CrGl3.2Cr03). 

(KCl, + 2Cr03). 

Bichromate of chloride of potassium 

(KCl + 2Cr03). 
Bichromate de chlorure de potassium, 

or chlorochromate de potasse 

(KC1.2CrO='). 



19. 
20. 
21. 
22. 

23. 



24. 
25. 

26. 
27. 
28. 
29. 
30. 



Zweifach chromsaures Chlorkalium 
(KaCl,2Cr03). 

Bichromate of chloride of potassium 
(KCl,2Cr03). 

Bichromate de chlorure de potas- 
sium, or chlorochromate de potasse. 



Chromochloride of potassium, 1863. 

Potassium chromatochloride, 

1872. 
Potassium chlorochromate, 1875 
L and 1879 (KCl,Cr03). 



Bichromate de chlorure de potassium. 



31. Chlorchromsaures Kali 



32. 
33. 



34. 
35. 
36. 



(crO^Sl). 



Bichromate of chloride of potassium, 
or potassic chlorochromate (KCl, 
Cr03?). 

Potassium chlorochromate (KCrOjCl). 

Potassium chlorchromate. 



vni. 



1. Nitrat of lead. 

2. Nitrate of lead. 

3. Subnitrate of lead. 

4. Subnitrate of lead. 



5. Dinitrate of lead. 

6. Dinitrate of lead (2PL -i- n'). 

7. Nitras biplumbicus (Pb^isfj. 



ON CHEMICAL NOMENCLATUEE. 



271 



8. 
9. 

10. 
11. 

12. 

13. 



14. 
.16. 



16. 

17. 

18. 
19. 
20. 
21. 
22. 



Dinitrate of lead ((2PL + n'). 
Bibasic nitrate of lead (PbO,N05 + 
PbO). 



Basisch salpetersaures Bleioxyd 

(Pb-^). 
Zweifach basisch salpetersaures 
Bleioxyd (2PbO,5f05, or 2PbO, 
NO3.HO). 

Basic salt, containing two atoms of 

oxide of lead united to one of 

nitric acid. 
Bibasic nitrate of lead (PbO,N05 + 

PbO). 
Sous-azotate de plomb ; azotate bi- 

basique (2PbO.N05+ HO). 
Basic nitrate. 

Halbsaures Salz (PbO.HO.PbO.NOj). 
Dinitrate of lead (2PbO,N05). 
(See 17). 



23. 



24. 



25. 
26. 

27. 
28. 



29. 
30. 



31. 

32. 
33. 

34. 
35. 

36. 



Basic nitrates of lead ; diplumbic 

nitrate. 
Azotate basique de plomb 

Basic nitrate. 

Plumbic hydronitrate (PbNOaHO). 

Azotate diplombique (Az03)„Pb,PbO 
or parazotate, (Az20,)Pb2, or 
orthoazotate (AzOi)"'Pb"H'. 

Halbgesattigt hydratisch basisch 
Salpetersauresblei. 

Basisches Salz r^y^jOjPbY 

Basic nitrate. 

Dibasic plumbic nitrate (Pb2N0,, 

PbHoO„). 
Basic nitrate, Pb(N03)0H. 
Plumbic nitrate hydrate, NO, 

(OPb"Ho). 
Basic salt. 



rx. 



10. 
11. 

12. 

13. 

14. 

15. 
16. 
17. 
18. 
19. 



Submuriat of lead. 
Submuriate of lead. 
Submuriate of lead. 



Oxychloride of lead. 
Bibasic chloride of lead (PbCl + 
2PbO), Tribasic (PbCl + 3PbO). 



Einfach-, zweifach-, &c. basisches 
Chlorblei (PbCl + PbO), &c. 



Oxychloride of lead. 
Oxychlorure. 

Basische Bleichloride, Oxychlorid, 
Bisoxychlorid, &c. (PbO.PbCl, 
2PbO,PbCl, &c.) 



20, 
21. 
22. 
23. 

24. 
25. 
26. 
27. 

28. 
29. 

30. 

31. 
32. 
33. 

34. 
35. 
36. 



Oxychlorides of lead (PbO,PbCl, &c.) 
Oxychlorure. 

Oxychlorides (Pb^Cl^O or PbCLPbO, 

&c.), 1881, III. Supp. 
Oxychlorures de plomb. 

Oxychlorides PbCL.PbO, &c.) 
Basic plumbic chlorides (Pb.,OCL, 
Fhfifi].,., &c.) 

Oxychlorides of lead (PbCL.PbO, 

&c.) 
Diplumboxydchloriir ; Triplumb- 

dioxydchloriir, &c. 
Basische Salze. 

Oxychlorides (PbCl2,PbO, &c.) 
Oxychlorides of lead (PbO.PbCl,, 

&c.) 
Basic chlorides (PbClj + PbO, kc.) 
Oxychlorides. 
Oxy- or basic chloride. 



X. 



Subnitrate of bismuth. 
Subnitrate of bismuth. 

Tetartonitrate of bismuth. 
Hydrated subnitrate of bismuth. 

Hydrated subnitrate of bismuth. 
Subnitrate of bismuth (HO.NO. 
+ 3BiO). 



10. Salpetersaures Wismuthoxyd, ein- 

fach. Basisch salpetersaures Wis- 
muthoxyd (Bi03,N05-(-Aq). 

11. Basisch salpetersaures Wismuth- 

oxyd ; Bismuthum Subnitricum 
(NA.BiO + 3Bi0,Aq.N,0.,Bi0 
+ 2Bi0). 

12. Verbindung von salpetersaurem Wis- 

muthoxyd mit Wismuthoxydhy- 

drat (BiN + SBiS). 



272 



REPOET 1885. 



13. Basisch salpetersaures Wismuthoxyd, 

drittelsaures salpetersam-es Wis- 
muthoxyd. 

14. Basisch salpetersaures Wismuth. 

15. A basic salt (BiOa + NOj). 

16. Subnitrate of bismuth (BiOa.NO^ 

+ H0). 

17. Sous-azotate de bismuth. 

18. Basic nitrate of teroxide of bismuth 

(Bi03,N05 + 2HO). 

19. Drittelsaures Salz (BiOa.NO^ + 2H0), 

Bisoxynitrat 

(2(Bi03,3HO)Bi03,3N05). 
Subnitrate of bismuth (9HO,4N05, 

+ SBiOa). 
Sous-azotate de bismuth. 



20. 

21. 
22. 

23. 

24. 
25. 



1. 
2. 
3. 

4. 
5. 
6. 

7. 

8. 

9. 

10. 



11. 
12. 
13. 



14. 

15. 

16. 

17. 

18. 



9. 
10, 



A basic nitrate (BiNO^.H^O or 

Bi„03,NA.2H,0). 
Sous-azotate. 



26. Basic nitrate (Bi„03,N„05,20H„, or 

Bi" (N03)3,Bio03',30H;). 

27. — 

28. Azotate basique de bismuth (Bi'" 

(AzO,) + H,0 or (BiO) AzO, 
+ H„0). 

29. Basic nitrate of bismuth, also called 

trisnitrate of bismuth (Bi^Oj, 
NA.H.O). 

30. Wismuthnitrat. Bi(0N0„)(0H)2. 

31. Basisches salpetersaures Wismuth- 

oxyd T^jj^logBi or NOjOBiO 

+ H..0). 

32. Basic nitrate (see 26). 

33. Bismuthous subnitrate (Bi„03, 

2HNO3). 

34. Basic bismuth nitrate, Bi (OH)^ 

NO3. 

35. Bismuthous nitrate dihydrate, NOj 

(Bi"H020). 

36. Basic bismuth nitrate, Bi(OH)2N03. 



XI. 



A subsalt. 
A compound of 
with chloride. 



oxide of bismuth 



(See 6.) 

A subsalt (BiCl -1- 2 BiO -1- HO) 

Wismuthoxyd - chlorwismuth. Wis- 
muthoxychloriir. Basisch salz- 
saures Wismuthoxyd (BiClj, 
2Bi03). 

Basisches Salz. 

(BiCl + 2BiH). 

Wismuth Bisoxychlorid. Zweifach- 
basisches Wismuth Chlorid 
(Bi„ei0j Oder Bi^eia + BiA)- 

Oxychloride of bismuth (BiCla + 

2Bi03 + 3HO). 
Oxychloride of bismuth (BiCl3, 

2Bi03). 
Oxychlorure de bismuth (Bi.,Cl3 + 

2(Bi„03 + 3H0). 



Oxysulphat of mercury. 
Suboxysulphate of mercury. 
Neutral persulphate of mercury. 
Suboxysulphate of mercury. 
Disulphate of mercury. 
A sub-salt. 

A sub-salt. 
(HgO.S03 + 2HgO). 
Schwefelsaures Quecksilberoxyd, 
Drittel (SHgO.SOj). 



XII. 



19. Bisoxychlorid, zweifach basisches 

Salz (2Bi03,BiCl3). 

20. Oxychloride of bismuth (BiClj, 

2Bi03). 

21 (See 17.) 

22 — 

23. Oxychloride of bismuth (BiOCl), 

1863. Bismuthyl chloride 

(BiOCl), 1879. Supp. III. 

24. Oxychlorure (BiOCl). 

25. Basisches Chlorwismuth. 

26. Oxychloride (BiClO). 

27. Bismuth oxychloride (BiOCl). 

28. Oxychlorure de bismuth (BiOCl or 

Bi.,03,BiCl3). 

29. Oxychloride of bismuth, 2(BiCl3, 

Bi203),H„0. 

30. Wismuthoxychloriir. 

31. Basisches Chlorwismuth, Wismuth- 

oxycblorid (BiOCl). 

32. Oxychloride (BiClO). 

33. Bismuthous oxychloride, 2(BiCl3 

Bi,,03),0H„ or BiOCl. 

34. Bismuth oxychloride (BiOCl). 

35. Bismuthous oxychloride (BiOCl). 

36. Basic bismuth chloride. (Bismuth 

oxychloride.) 

1 1 . Basisches schwefelsaures Quecksilber- 

oxyd (SHgO.SOa). 

12. Basisches schwefelsaures Quecksilber- 

oxyd. 

13. Basisch schwefelsaures Quecksilber- 

oxyd (3HgO.S03). 

14. Basisches schwefelsaures Queck- 

silberoxyd. 

15. Basic sulphate (3HgO + SO3). 

16. Sub-sulphate. 

] 7. Sel basique (3HgO.S03). 



ON CHEMICAL NOMENCLATURE. 



273 



'.SO3). 



18. A basic salt (SRgO.SOj). 

19. Drittelsaures Salz (3HgO.£ 

20. A sub-salt (SHgO.SO,). 

21. Sel basique (SHgO.SO'). 

22. — 

23. Basic sulphate of mercury (SHgO.SOj 

= HgSO,.2HgO). 



24. Sel basique 




25. — 

26. A basic salt (SHgO.SOj). 

27. A basic salt (HgjSOs). 

28. Sulfate trimercurique(SOjHg,2HgO). 

29. A basic sulphate (HgO.SO3.2HgO). 

30. Drittelgesattigtes Mercuridsulfat. 

31. Basisches Salz(SOj02Hg + 2HgO). 

32. A basic salt (3HgO.S03). 

33. A basic salt (HgS04.2HgO). 
31. A basic salt (Hg3S06). „ 

35. Trimercuric sulphate (SHgOj). 

36. Basic sulphate (SOj.OjHg + 2HgO). 



10. 



11. 



12. 

13. 

14. 
15, 
16, 

17, 



xm. 

18. 
19. 



Chlorosulphuret of mercury (hg + 

2C)-i-2(hg + 2S). 
Chloride and sulphuret of mercury 

(HgCl + 2HgS). 
C h 1 o r q u ecksilber- Schwef elquecksil- 

ber, Oder Chlor- und Schwefel- 

quecksilber (2HgS,HgCl). 
SchwefelbasischesQuecksilberchlorid 

(Berzelius' nomenclature) (HgClj 

+ 2HgS). 
Quecksilberschwefelchlorid (Hg€}, 

+ 2HgS). 



Chlorosulphuret (HgCl + 2HgS). 
Sulphochloride of mercury (HgCl, 

2HgS). 
HgCl + 2HgS, 



20. 
21. 
22. 
23. 

24. 
25. 

26. 
27. 

28. 

29. 

30. 
31. 
32. 
33. 
34. 
35. 



Quecksilbers ul p huretochlorid 
(Quecksilber chlorosulphuret) 
(2HgS,HgCI). 

(See No. 17.) 

Sulphochloride of mercury (Hg.S, 

cy. 



Mercuric sulphochloride (HgjSjClj). 
Sulfochlorure mercurique C2HeS, 

HgCL). 
Chlorosulphide of mercury (HgCl~ 

2HgS). 
Mercuridthiochloriir. 



(2HgS,HgCl,). 

Trimercuric disulpho- /HgClrr \ 
dichloride VHgCl^s^ 



36. — 



1. 

2. 

3, 

4. 

5. 

6, 

7. 

8. 

9. 
10. 
11, 



12. 
13. 



14, 

15. 
16. 



Sulphoantimoniate. 
Sulphostibias natricus (Na Sb2). 

FiinfEachschwefelantimonnatrium, 
Antimon persulphid-Natriimi ( S ulpho- 

stibias natricus cum aqua) (Sb^Sj, 

NaS + 12Aq) . 
Natrium antimon Sulphid (3 NaS + 

SbSJ. 
Antimonpersulphid-Natrium. Anti- 

monpersulphid - schwefelnatrium, 

&c., &c. (Sb^Sj.NaS). 

Sulphantimoniate (3NaS.SbS.), 
1885. 



XIV. 
17. 

18, 
19, 



20. 

21. 

22. 
23. 

24. 

25. 
26. 

27. 

28. 

29. 
30. 



Sulfantimoniate de sulfure 
Sodium (3NaS.Sb2S3). 



de 



Natrium sulphantimoniat (3NaS, 

SbSj). 
Sulphantimoniate of sodium (3NaS, 

SbS,). 
Sulfantimoniate de sulfure de sodium 

(SNaS.SbjSJ 

Sulphantimonate of sodium (NaaSbS- 
or 3Na2S.Sb2S5). 

Sulphantimoniates (Sb^S^SMoS or 

SbS^M,). 
Sodic sulphantimoniate (SbS^Naj). 
Sulfo-antimoniate de sodium (SbS. 

Na3). 
Sulphantimoniate. 
Natriumthioantimonat (Na,SbSJ, 



274 



REPORT— 1885. 



31. SbS^Naa, or (SbS) SaNa,. 

32. Sodium- sulphantimonate. 

33. Trisodic sulphantimoniate (Na^SbS^). 

34. Sodium thioantimonate (NajSbS,). 



35. Trisulphosodic sulphantimonate (Sb 

S"Nas3). 

36. — 



XV. 



1. 

2. 

3. 
4. 
5. 
6. 

7. 

8. 



10. 
11. 

12. 
13. 
14. 
16. 

16. 

17. 

18. 

19. 



Fluat of potass and silica. 
Fluate of potash and silica. 
Fluosilicate of potash. 
Silico-fluate. 
Fluosilicate of potash. 
Silicofluoride of potassium (po + 2Si 
+ 3f). 

Silicofluoride of potassium (po + 2Si 
+ 3f). 

Double fluoride of silicon and potas- 
sium (2SiF3,3KF). 

Fluor-siliciumkalium (KF,SiFj). 

Fluorsiliciumkalium. Kieselfluor- 
kalium (SKF^/iSiFs). 

Fluorkiesel Kalium. 

Kalium-Kieselfluorid (3KF,2SiP3). 

Fluosilicate of potassium, silico- 
fluoride of potassium (SiF^ + KF). 

Double fluoride of silicon and 
potassium (2SiF3,3KF). 

Hydrofluosilicate de j^otasse (3KF1, 
2SiFl3). 

Double fluoride of silicium and 
potassium (SKF.SiF,). 

Kieselfluorkalium. Fluorkieselkalium 
(3KaFl,2SiFl3, oder KaFl.SiFlJ. 



20. 

21. 

22. 
23. 

24. 

25. 
26. 

27. 
28. 
29. 

30. 
31. 
32. 

33. 
34. 

.35. 

36. 



Silicofluoride of potassium (KF, 

SiF.). 
Hydrofluosilicate de potasse (3KF1, 

2SiFl3). 

Silicofluoride of potassium. Potassic 
silicofluoride (2KF,SiFj). 

Fluorure double de sihcium et de 
potassium. 

Kieselfluorkalium. 

Double fluoride of silicium and 
potassium (2KF,SiFJ. 

Potassic fluosilicate (K.jSiFg). 

Fluosilicate de potassium. 

Silicofluoride of potassium (2KF, 
SiF,). 

Metallsilicofluoriire. 

Kieselfluormetalle (SiF^.MFj). 

Double fluoride of silicium and 
potassium (2KF,SiF,). 

Potassic silicofluoride. 

Silicofluoride. potassium fluosili- 
cate (K^SiFg). 

Potassic silicofluoride (SiFjK2 = Si 
F„2KF). 

Potassium fluosilicate. 



XVI. 



1. 
2. 
3, 

4. 
5. 
6. 

7. 
8. 



10. 

11. 
12. 
13. 
14. 
15. 



16. 
17. 



Muriat of platinum and potass. 
Muriate of platinum and potash. 



Bichloroplatinate of potassium. 
Platino-bichloride of potassium 
(pi + 2c) + (po + c). 

Platino-bichloride of potassium 

(pl+2c) + (po-i-c). 
Chloride of platinum and jjotassium 

(KCl + PtClj). 
Zweifach Chlorplatinkalium (KC1 + 

PtCU). 
Kaliumplatinchlorid (KClj + PtClJ. 
Kaliumplatinchlorid. 
Kalium-platinchlorid (KOi + PtGi^)- 
Platinchlorid-chlorkalium. 
Double salt of bichloride of platinum 

with chloride of potassium (KCl 

+ PtCL). 
Chloroplatinate of potassium (KCl, 

PtClj). 
Chlorure double de platine et de 

potassium (PtCl, + KCl). 



18. 

19. 

20. 

21. 

22. 
23. 

24. 

25. 
26. 

27. 
28. 
29. 

30. 
31. 
32. 



Bichloride of platinum and chloride 

of potassium (PtClj.KCl). 
Kalium-platinchlorid. Kalium-chlo- 

roplatinat (KaCl.PtClj). 
Double chloride of platinum and 

potassium (KCl.PtCl,,). 
Chlorure double de platine et de 

potassium (PtCL -i- KCl). 

Chloroplatinate of potassium, 1866. 

potassium platinochloride (KjPt 

CIJ. Supp. I. 1872. 
Chlorure double de platine et de 

potassium. 
Kaliumplatinchlorid. 
Potassium platinochloride (2KC1, 

PtCl,). 

Chloroplatinate de potassium. 

Platinochloride of potassium (2KC1, 
PtCl,). 

Kaliumplatinchlorid. 

Kaliumplatinchlorid (2KCl,PtCl4). 

Potassium platinochloride or chloro- 
platinate (2KCl,PtCl<). 



ON CHEMICAL NOMENCLATURE. 



275 



33. Potassic platinic chloride. 

34. Potassium platinichloride or chloro- 

platinate (KjPtClJ. 



35. Potassic platinic chloride (PtCl., 
2KC1). 

36. Potassium chlorplatinate. 



XVII. 



1. — 

2. — 

3. — 

4. — 

5. — 

6. Cyanuret of platinum and potassium. 

7. — 

8. Cyanuret of platinum and potas- 

sium. 

9. Platino-cyanide of potassium (K, 
PtCy^ + SHO). 

Einfach-cyanplatinkalium (KCy, 
PtCy). 



10. 

11. 

12. 

13. 

U. 
15. 

16. 

17. 

18. 



1. 
2. 
3. 
4. 
6. 
«. 
7. 
8. 
9. 

10. 

11. 



12. 

13. 
14. 
15. 



16, 
17. 



Kalium Platincyaniir (K6y, + Pt6y 

+ 3H). 
Kalium Platincyaniir (K6y + Pt€y 

+ 3H0). 

Platinocyanide of potassium (PtCy 
+ KCy or K,Cpty). 

Platinocyanides (MCy.PtCy). 

Cyanure double de platine et de po- 
tassium (KCy + PtCy + 3H0). 



19. 

20. 
21. 

22. 

23. 



24. 
25. 
26. 

27. 

28. 

29. 
30. 
31. 
32. 
33. 
34. 

35. 
36. 



Kaliumplatincyaniir 
-(-3H0). 



(KaCy.PtCy 



XVIII. 

18. 
19. 



20. 
21. 
22. 
23. 



Acetate and arsenite of copper, 

CuO, (C^H303) + 3 (CuO.AsOj). 
Essigarsenigsaures Kupferoxyd, 

3(CuO,As03) + C^HjCuO^. 
Essigsaures Kupferoxid und Arsenig- 

saures Kupferoxid, A,CuO 

+ 3(As03, CuO). 
Arsenichtsaures und essigsaiires 

Kupferoxyd, (CuA + 3Cu-As). 
Arsenigessigsaures Kupferoxyd. 

Compound of acetate of copper, 
and arsenite of copper, CuO.A 
-f-3(H0.2CuO-hAs03). 

Acetate and arsenite of copper, CuO, 
(C^H303) + 3 (CuO.As,03). 

Une combinaison, CuO. C.H3O3 
+ 3(2CuO.AsO,). 



24. 
25. 
26. 

27. 

28. 
29. 
30. 

31. 

32. 
33. 

34. 

35. 
36. 



Cyanure double de platine et de 
potassium (KCy -1- PtCy -t- 3H0). 

Platinocyanide of potassium (K..Pt 
Cy^ = 2KCy,PtCy,), 1866. Potassic 
platinous cyanide (KjPtCyJ. 
Supp. I. 1872. 



Plantinocyanure de potassium, (Pt 
CyOK- + 3H-0. 

Kaliumplatincyaniir. 
Kaliumplatincyaniir (2KCy,PtCy2). 



Potas.sium platinocyanide, K2Pt(CN). 
+ I2H2O. 

Potassium platinous cyanide. 



Eine Verbindung, CuO.AcOj 

+ 3(2CuO,A.s03). 
CuO,CjH303 + 3 (CuO.AsOj). 
CuO,C,H303 + 3 (2Cu0,As03). 

Aceto-arsenite of copper (CoHjOj)^ 
Cu", 3 (As02)2 Cu" or C^H.O*. Cu"0 
+ 3 (AsACu"0). 



Cupric acetoarsenite, Cu(As02) 

(C2H3O2). 
Un acetoarsenite. 

Arsenigessigsaures Kupfer, 
Cu.,(OAsO) 3 (OC2H3O). 



Cupric arsenite and acetate, 

SCuAsjOj. Cu (CjHjO^),. 
Copper acetoarsenite, SCuASjO. 

+ Cu(C2H302)2. 

Double compound. 



T 2 



276 REPOET — 1885. 

RepoH of the Committee, consisting of Professors Odllxg, Hunt- 
ington, and Hartley, ai^'pointed to investigate by means of 
Photography the Ultra-Violet Spark Spectra emitted by Metallic 
Elements, and their combinations under varying conditions, 
Braxon up by Professor W. N. Hartley, F.R.S. {Secretary.) 
The last Report of this Committee was presented at the Sotithport meet- 
ino- of the British Association ; since then an investigation in detail has 
bera prosecuted of the changes observable in photographs of the spectra 
of the metals when a series of solutions of definite strengths is examined. 
It had previously been shown that solutions containing the same element 
in different proportions emit variations of the same spectrum, the lines 
differing in number, length, and intensity ; and the converse— namely, 
that under the same spark conditions similar solutions of the same 
strength always emit the same spectrum. Furthermore, I have shown 
the invariable character of the cadmium, tin, lead, and magnesium lines by 
observations made on about five thousand photographs, including not 
fewer than two hundred examples of other metals. The reason of this 
arises from the fact that unless the spark be almost at the highest tempera- 
ture attainable, its emissive power is insufficient to affect the photographic 
plate in the usual period of exposure ; it follows from this that when a 
condenser of constant capacity is in circuit, variable conditions such as 
may be introduced by the electrodes being near together or far apart, or 
by the use of a large or small coil, do not affect the result. Sparks are 
shortened and the character of the spectra is greatly altered by the use 
of a coil with a stout secondary wire, an instrument introduced and 
employed by M. Eugene Demarfay. The use of an instrument of this 
kind is not well adapted to the photographic method of working, because 
the nature of the sparks is such that the graphite electrodes are rapidly 
burnt away and the sparks are very short. 

For the examination of solutions chlorides are generally employed, 
but sulphates and nitrates are also used. The electrodes are nearly 
always of graphite (' Phil. Trans.' p. 52, Part I. 1884) ; sometimes gold,, 
copper, or platinum electrodes are required for special purposes, wires of 
the metal being twisted into wicks. 

The solutions examined generally contained 1 per cent., -^i\ xrcrtn, 
and ToW*^ °f metal. It is seldom that more than three or four lines 
are visible in solutions of the latter dilution, and the rapidly diminishing 
number of lines in solutions weaker than -^^ih per cent, is very striking. 
In the following tables the spectra corresponding to various solutions are 
given, and attention is particularly directed to the copper, silver, and tin. 
spectra as illustrating this point. In many spectra it is impossible to 
predict the line or lines which will be found to be the most persistent. 
It ia also noticeable that the alteration of lines consequent on the dilution 
of solutions is variable in character with different lines in the same 
spectrum. Generally speaking, long lines shorten until they disappear, 
sometimes they become attenuated before they shorten, and in other cases 
they attenuate until they fade away altogether. 

The calcium lines H and K attenuate considerably before they shorten,, 
while the lines of copper with wave-lengths 3273-2 and 3246-9, and of 
silver, 33828 and 3280-1, attenuate and fade almost away before 
shortening. 



ON THE DLTBA-VIOLET SPAEK SPECTRA. 



277 



Several examples could be quoted of the analysis of minerals made 
by the spectroscope, the metallic constituents being estimated quantita- 
tively with exactitude and great faciUty. In some cases the results 
obtained by the spectroscope inspire greater confidence than those made 
by ordinary methods. 

The descriptive tables which follow are intended to be used with 
maps drawn to the scale of wave-lengths, and to a scale of actual mea- 
surements taken from photographs, so that the lines may be readily 
identified. The scale numbers given in the tables in hundredths of an 
inch refer to photographs such as those published in the ' Journal of the 
Chemical Society ' (' Trans.' vol. xli. p. 90, 1882), from which actual 
measurements may be taken -with an ivory scale. 

The limit of sensitiveness of the spectrum reaction is perhaps the 
greatest in the case of magnesium ; one part of the metal in 10,000 
millions of solution is easily detected by the appearance of the lines with 
wave-lengths 2801 "6 and 2794"1 attenuated and shortened. By increasing 
the strength of the spark the sensitiveness may be magnified 10,000 fold. 

It was shown in the Report presented in 1883 how spectrum observa- 
tions may be applied to determining the atomic weight of an element. 
Taking into account the spectrum of berylUam, this metal could find no 
place among the triad elements, but naturally took a position at the head 
of the dyad group. According to the periodic law its atomic weight 
would thus have the value 9. This view was opposed at the time, but it 
is satisfactory to learn that it has since been completely confirmed by the 
experimental work of Messrs. Nilson and Pettersoa and Dr. Humpidge. 

The Zinc Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 
108-49 
113-75 
116-30 
145-69 
194-98 
252-31 
267-95 


3344-4 
3301-7 
3281-7 
3075-6 
2800-1 
2557-3 
2501-5 


3344-4 

3301-7 

3281-7 

3075-6 

2800-1 ? 

2557-3 

2501-5 


3344-4 
3301-7 
3281-7 



The Thallium Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 

64-55 

88-7 
143-0 
172-21 
201-87 
259-86 
335-27 


3775-6 
3518-6 
3091-0 
2917-7 
2767-1 
2530-0 
2299-3 


3775-6 
.3518-6 
3091-0 

2767-1 
2530-0 
2299-3 


3775-6 
2767-1 



278 



EEPOET 1885. 



The Cadmium Spectrum. 







Wave-lengths 




Scale numbers 










1 per cent. 


0-1 per cent. 


0-01 per cent. 


0-001 percent. 


Hundredths of an inch 










79-37 


/ 3612-0 
\ 3609-6 


36120 


3612-0 




79-68 


3609-6 


3609-6 




94-30 


/ 3466-7 
\ 3465-2 


3466-7 


3466-7 




94-50 


3465-2 


3465-2 




101-45 


3402-8 


3402-8 






1190 


3260-2 








205-87 


2747-7 


2747-7 






248-24 


2572-3 


2572-3 






326-8 


f 2321 -6 
2313-5 








329-85 


2313-5 


2313-5 




339-25 


■ 2288-8 
2265-8 


2288-8 


2288-8 




348-15 


2265-8 


2265-8 


2265-8 


377-48 


2196-4 








400-2 


2146-8 









The Aluminium Spectrum. 







Wave-lengths 


Scale numbers 






1 per cent. 


0-1 per cent. 


0-01 per cent. 


0-001 per cent. 


Hundredtlis of an inch 










f 49-85 
1.51-16 


/ 3960-9 


.3960-9 


3960-9 


3960-9 ? 


1.3943-4 


3943-4 


3943-4 


3943-4 ? 


The air-lines conti; 


^uous to the abo\ 


-e are very strong, hence it is a little doubtful 


whether they are pres 


ent in the spectr 


um of a solution so dilute as 001 per cent. 


/ 70-02 
171-05 


f 371 3-4 
13701-5 














r 79-17 
180-5 


f3612-4 
13601-1 


3612-4 


3612-4 




36011 


3601-1 




82-07 


3584-4 








r 142 86 
1.144-5 


/ 3091-8 


.3091-8 


3091-8 


.3091-8 


1.3081-2 


3081-2 


3081-2 


3081-2 


148-5 


3056 6 








191-76 


2815-3 


2815-3 


2815-3 


2815-3 


226-3 


2659-3 


2659-3 






228-26 


2651-2 


2651-2 






249-66 


2566-9 


2566-9 






308-55 


2373-3 








309-0 


2372-0 








309-6 


2370-2 








309-94 


2367-2 








310-62 


2364-5 









The line with -wave-lengtli 3584"'4 is both much longer and stronger 
than either 3612'6 or 3601-2, yet it is not so persistent. From appear- 
ing as a strong line it disappears rather suddenly. 

The line -v^ith -wave-length 28153 is the strongest in this epectrum. 



ON THE ULTRA-VIOLET SPARK SPECTRA. 



279 



Tabular Description of the Spectra characteristic of Solutions 
containing Magnesium. 







Wave-lengths of the lines visible 


Scale numbers 




Parts of magnesium per 100 of solution 


10 


1 


0-1 


0-03 


0-02 


0-01 


0-003 


0-002 


0-001 




per cent. 


per 


per 


per 


per 


per 


per 


per 


per 






cent. 


cent. 


cent. 


cent. 1 cent. 


cent. 


cent. 


cent. 


Hundredths 




















of an inch 




















17-46 


4480 


4480 


4480 














69-30 


r 3837-9 


3837-9 


3837-9^3837-9 


3837-9 










59-83 


■{ 38321 


38321 


3832-1*3832-1 


3832-1 










60-07 


3829-2 


3829-2 


3829-2 














142-3 


r 3096-2 
■I 3091-9 
L 3089-9 


3096-2 


3096-2 














142-85 


3091-9 


3091-9 














143-18 


3089-9 


3089-9 














168-7 


/ 2935-9 
\ 2928-2 


2935-9 


2935-9 


2935-9 


2935-9 2935-9 


2935-9 


2935-9 


2935-9 


170-18 


2928-2 


2928-2 


2928-2 


2928-2 2928-2 


2928-2 


2928-2 


2928-2 


184-63 


2851-2 


2851-2 


2851-2 


2851-2 


2851-2 2851-2 


2851-2 


2851-2 


2851-2 


194-55 


r2801-6 


2801-6 


2801-6 


2801-6 


2801-6 2801-6 


2801-6 


2801-6 


2801-6 


195-39 


I 2796-9 


2796-9 


2796-9 


2796-9 


2796-9 2796-9 


2796-9 


2796-9 


2796-9 


195-95 


' 2794-1 


2794-1 


2794-1 


2794-1 


2794-1 2794 1 


2794-1 


2794-1 


2794-1 


196-92 


[2789-6 


2789-6 


2789-6 


2789-6 


2789-6 2789-6 


2789-6 


2789-6 


2789-6 


198-64 


(-2781-8 


2781-8 


2781-8 


2781-8 


1 








198-96 


2780-2 








1 








199-3 


.' 2778-7 


2778-7 


2778-7 


2778-7 


2778-7 2778-7 








199-61 




2776-9 
















199-97 


I2775-5 


2775-5 


2775-5 













A line ma}' be shortened or -weakened, but its -wave-length in this table denotes 
that although it may be changed it is still visible. The numbers bracketed are the 
wave-lengths of characteristic groups of lines. 



The Indium Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


001 per cent. 


Hundredths of an inch 

15-88 

39-91 
119-31 
119-68 
151-35 
168-00 
177-34 
214-56 
251-76 
332-2 


4510-2 
4101-3 
3257-8 
3255-5 
3038-7 
2940-8 
2889-7 
2709-3 
2559-5 
2307 


4510-2 
4101-3 

3255-5 

3038-7 

2940-8 

2889-7* 

2709-3 

2307 


3255-5 
3038-7 



This is barely visible. 



280 



EEPORT — 1885. 



The Copioer Spectrum. 







Wave-lengths 


Scale numbers 






1 per cent. 


0-1 per cent. 


0-01 per cent. 


0-001 per cent. 


Hundredths of an inch 










11310 


3306-8 


3306-8 






115-10 


3289-9 








r 117-25* 


/ 3273-2 
13246-9 


3273-2 


3273-2 




1 120-7 


3246-9 


3246-9 


3246-9 


164-53 


2959-5 








190-13 


2823-2 








201-36 


2769-1 


2769-1 






211-8 


2721-2 








212-65 


27] 8-4 


2718-4 






213-7 


2713-0 


2713-0 






2161 - 


2702-7 








216-58 


2700-5 








219-37 


2688-8 


2688-8 






224-7 


2666-7 








236-45t 


2617-8 








241-1 


2599-7 








241-58 


2598-3 








255-94 


2544-6 


2544-6 






260-25 


2528-8 


2528-8 






261-00 


2526-2 








266-77 


2506-2 


2506-2 






270-91 


2491-4 








271-65 


2489-1 








272-72 


2485-6 








276-45 


2473-2 








298-31 


2403-3 








299-4 


2400-1 








r309-17 
\ 309-57 


/2371-6 
12370-1 


2371-6 






2370-1 






336-8 


2295-0 








343-67 


2277-0 








r356-27t 


r2248-2 
2247-7 


2248-2 






j 355-5 


2247-7 






] 357-1 


2244-0 
2243-5 


2244-0 






L357-32 


2243-5 





* This pair of lines differs from all others in the spectrum by not being shortened 
on dilution, but becoming attenuated till at last they disappear. They remain long 
lines till the last. 

f This is a very fine and very long line. 

X This group is distinctly seen to be composed of four lines in the photographs 
of the 1 per cent, solution, and some lines, to the number of four or five, more 
refrangible than these are visible. 



ON THE ULTEA-VIOLET SPARK SPECTRA. 



281 



The Silver Spectrum. 







Wave-lengths 




Scale numbers 










1 per cent. 


0-1 per cent. 


0-01 per cent. 


0-001 per cent. 


Hundredths of an inch 










103-94 


3382-3 


3382-3 


3382-3 




116-45 


3280-1 


3280-1 


3280-1 




168-5 


2937-6 








169-3 


2933-5 


2933-6 






170-17 


2928-2 


2928-2 






175-02 


2901-6 








176-07 


2895-6 








180-44 


2872-7 


2872-7 






191-82 


2814-5 








195-03 


2798-8 








201-81 


2766-4 


2766-4 






204-2 


2755-5 








214-22 


2711-3 


2711-3 






226-27 


2659-6 


2659-6 






227-08 


2656-2 








246-3 


2579-9 








268-81 


2506-0 


25060 






274-52 


2479-9 








275-41 


2476-8 








276-41 


2473-3 


2473-3 






279-92 


2462-2 








280-52 


2459-8 








282-6 


2453-0 








284-38 


2447-4 


2447-4 






287-46 


2437-3 


2437-3 


2437-3 




290-0 


2429-8 


2429-8 






293-08 


2419-9 


2419-9 






295-35 


2413-3 


2413-3 


2413-3 


2413-3 


295-94 


2411-3 


2411-3 






297-94 


2406-4 








298-85 


2404-5 








301-10 


2395-7 








302-74 


2390-8 








304-07 


2386-7 








305-25 


2383-6 








307-94 


2376-5 








311-70 


2364-3 








312-34 


2362-3 








313-47 


2359-2 


2359-2 






313-88 


2358 


2358-0 






323-35 


2331-7 


2331-7 


2331-7 




325-73 


2325-3 


2325-3 


2325-3 




327-37 


2320-5 


2320-5 


2320-5 




328-59 


2317-4 


2317-4 


2317-4 




342-55 


2280-7 


2280-7 






354-95 


2249-9 


2249-9 






354-90 


2247-6 


2247-6 


2247-6 




362-86 


2230-6 









282 



REPORT 1885. 



The Mercury Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 
r 74-6 
< 75-37 
L 77-37 
r 137-08 
i 137-95 

163-37 

185-45 

258-75 

364-51 


f 3662-9 

{ 3654-4 

L3632-9 

/3130-4 

13124-5 

2966-4 

2846-8 

2533-8 

2225-7 


3632-9 

3130-4 
2966-4 

2533-8 


2533-8 









The Tin Spectrum. 








Wave-lengths 




Scale numbers 








1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 








62-40 


3800-3 


3800-3 




ri07-51 


'3351-8 
J 3329-9 


3351-8 




1 110-25 


3329-9 




1 11603 


' 3282-9 
3261-6 


3282-9 




tll8-83 


3261-6 




130-7 


3174-3 


3174-3 




/152-18 
1156-29 


/ 3033-0 
13007-9 


3033-0 




3007-9 




173-05 


2912-0 






176-18 


2895-0 






177-8 


2886-9 






ri82-47 


r28620 


2862-0 


2862-0 


\ 184-99 


{ 2849-2 






Ll87-01 


L2833-9 


2833-9 




192-3 


2812-5 


2812-5 




198-28 


2784-0 






199-34 


2778-8 


2778-8 




215-35 


2705-8 


2705-8 


2705-8 




' 224-95 




'2664-2 








225-98 




2660-6 








226-56 




2657-9 


2657-9 




t 


229-67 


* 


2645-4 








230-23 




2643-2 


2643-2 






233-17 




2631-4 


2631-4 




'242-65 


"2593-6 






243-10 


2591-7 






248-70 


2570-5 


2570-5 




255-45 


2545-6 


2545-6 




r269-8 
1273-4 


f 2495-0 
12482-9 






2482-9 




/ 289-95 
1292-37 


/ 2429-3 
12421-8 


2429-3 


2429-3 


2421-8 




310-11 


2368-3 






314-85 


2355-0 


23550 




321-94 


2335-3 






328-34 


2317-9 






355-83 


2247-0 







ON THE IJLTEA-VIOLET SPARK SPKCTEA. 



283 





The Lead 


Spectrum. 






Wave-lengths 




Scale numbers 






1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 








42-93 


4057-5 


4057-5 




67-61 


3738-9 


3738-9 




72-69 


3682-9 


3682-9* 




76-8 


3639-2 


3639-2 




83-31 


3572-6 


3572-6 


3572-6 


170-45 


2872-2 


2872-2t 




188-37 


2832-2 


2832-2 




190-30 


2822-1 






225-41 


2662-5 


2662-5 




237-48 


2613-4 


2613-4 




247-08 


2576-4 






373-43 


2204-3 







The Tellurmm Spectrum. 







Wave-lengths 




Scale numbers 








1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of an inch 








103-9 


3382-4 


3382-4 




116-43 


3280-0 


32800 




117-35 


3273-4 


3273-4 




120-77 


3246 8 


3216-8 


3246-8 


176-24 


2894-3 






181-25 


2867-7 






183-4 


2857-0 






344-1 


2386-3 


2386-3+ 




304-92 


2383-8 


2383-8t 




355-18 


22480 






355-36 


2247-3§ 






35718 


2243-3 







The Arsenic Spectrum. 







Wave-lengths 




Scale numbers 










1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hundredths of au inch 






» 


183-04 


2859-7 






199-22 


2779-5 


2779-5 




316-6 


2350-1 






339-14 


2288-9 







This is an exceedingly poor spectrum. 

* Barely visible. -f Very faint. 

X These lines appear very distinctly and are continuous in a 1 per cent, solution. 

§ The two last lines are faint, 22433 exceedingly so. 



284 



REPORT — 1885. 
The Antimony Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


0-01 per cent. 


Hxmdredths of an inch 

67-63 

80-74 

90-21 
109-36 
118-21 
120-8 
122-87 
152-91 
179-29 
197-05 
241-65 
260-33 
330-37 


37390 
3597-8 
3504-6 
3336-4 
3266-6 
3246-6 
3231-6 
3029-0 
2877-1 
2789-6 
2597-2 
2527-6 
2311-8 


2877-1 
2789-6 
2597-2 
2527-6 


2877-1 
2597-2 



The Bismuth Spectrum. 



Scale numbers 


Wave-lengths 


1 per cent. 


0-1 per cent. 


0-01 per cent 


Hundredths of an inch 

63-1 

71-63 

80-99 

89-69 

98-4 
102-25 
146-85 
153-75 
158-98 
159-67 
168-52 
175-85 
183-91 
185-49 
294-66 


3792-7 
3695-3 
3595-7 
3510-5 
3430-9 
3396-7 
3067-1 
3023-8 
2992-2 
2988-1 
2937-5 
2897-2 
2854-8 
2846-1 
2414-8 


3067-1 
3023-8 
2992-1 

2897-2 
2854-8 
2846-1 


3067-1 



Report of the Committee, consisting of Professor Tilden, Professor 
W. Ramsay, and Dr. W. W. J, Nicol {Secretary), appointed for 
the pxLrpose of investigating the subject of Vapour Pressures and 
Refractive Indices of Salt Solutions. 

I. Molecular Volumes of Salt Solutions. Part 11.^ 

The molecular volumes have been determined of fiffcy-sLx solutions, 
comprising forty-seven salts of potassium, sodium, lithium, strontium, 
cadmium, cobalt, and nickel, -with chlorine, bromine, chloric, carbonic, 
sulphuric, nitric, orthophosphoric, metaphosphoric, acetic, oxalic, tartaric, 

• Published in PMl. Mag., 1884. 



VAPOUR PEESSUBES AND REFEACTIVE INDICES OP SALT SOLUTIONS. 285 

and citric acids. The previous results were completely confirmed. 
The law is as follows : — 

The molecular volume of a salt in dilute solution is a quantity com- 
posed of two constants, one for the metal and another for the salt radical. 
It follows that the replacement of one metal, or salt radical, by another 
metal, or salt radical, is always attended by the same volume charge no 
matter how they may be combined together. 

The presence or absence of water of crystallization in one or both of 
the salts has no effect on the above law ; it therefore follows that it has 
the same volume as_ the solvent water. Water of constitution, however, 
shows itself in solution by possessing a volume markedly different from 
that of the rest of the water. 

These results point to the presence in solution of what may be 
termed the anhydrous salt, in contradistinction to the view that a 
hydrate, definite or indefinite, results from solution ; or, in other words 
no part of the water in solution is in a position, relative to the salt', 
different from the remainder. ' 

II. Saturation of Salt Solutions. Part II. 

It is found that the molecular volumes of a series of solutions of 
different strengths of the same salt may be satisfactorily expressed bv 
the formula : — '' 

M. V. = 1800 + na + n'^ji - n^y. 

Where n = number of molecules of salt per 100 HgO, and a, 3 and y 
constants depending on the salt, ' 

r = na + n^j3 — n^y • 
and 

7* 

- = a + 7i/3 — n^y. 

n 
This last is the mean molecular volume of the salt in solution. The 
curve is a parabola, and is such that ^ = twice the solubility of the salt 

in question .'. |i^ = solubility ; but this is also the apex of the parabola -^ 

saturation is therefore reached when the further addition of salt would 
produce dimmution of the mean molecular volume of the molecules 
already present. The last molecule before saturation, enters into solution 
with a volume sensibly equal to the mean, as is shown thus .- 

(«« + n^^ - n^y) - ((n - l)a + {n- 1)^/3 - (» _ 1)3^) ^ „ ^ ,^^ _ ^^2^^ 

When n = 'l±l. 
2y 

III. Supersaturation of Salt Solutions.^ 

In these papers experiments are described which lead to the con- 
clusion that the only truly supersaturated solutions are those which 
result from the fact that, when a hot solution is cooled, a finite time? 
IS required for the excees of salt to crystaUize out— what is usually 

' Published (1) Phil. Mag., June, 1885 ; (2) Phil. Mag., September, 1885, 



286 REPORT — 1885. 

termed supersaturation is not really so at all. Thus a distinctly super- 
saturated solution of sodium sulphate readily dissolves a quantity of 
the dehydrated salt when brought in contact with it without access 
of air. This sliows that the solution is not even saturated, much less 
supersaturated ; still this may be explained by the supposition that the 
constitution of a supersaturated solution is not the same as an ordinary 
one, inasmuch as heat is necessary for its preparation; the effect of 
heat being to decompose the decahydrate, no union of water and salt 
taking place in cooling. In the second paper it is shown that this 
is entirely a mistake. Supersaturated solutions are readily prepared 
in the cold by simply enclosing the dehydrated salt in a bulb, placing 
this in a bottle with the proper quantity of water, and, after closing, 
heating the bottle to 100° for a few minutes. When the whole is cold, 
the bottle is shaken, the bulb broken, and the salt readily dissolves. If 
excess of salt be used, the solution has the same percentage composition 
as one prepared by heating the decahydrate, and allowing it to cool with 
the excess of salt to the same temperature, air being excluded. It is 
further found that when the dehydrated salt is brought in contact with 
the water, as above described, no caking together is observable, the 
powdery condition being i-etained till solution is complete. Thus there 
is no hydration previous to solution, as is indeed shown by the possibility 
of preparing supersaturated solutions in this way, for were the smallest 
trace of the decahydrate produced such a solution, could not be formed. 
During the act of solution, however, considerable heat is evolved, which, 
as shown above, cannot be due to hydration, but may possibly result 
from the enormous contraction, about 40 per cent., undergone by the 
fialt. 

Finally, density determinations of solutions of Na2S04 and Na2S203, 
of various strengths, show that in passing the ordinary saturation point 
there is nothing to indicate any change in the constitution of the solution. 
The molecular volume steadily increases from the most dilute solution 
up to the most concentrated supersaturated solution examined, exactly 
as it does with an ordinary solution which is not capable of super- 
saturation. 

From these and other experiments it follows that a so-called super- 
saturated solution is simply a saturated or non-saturated solution of 
the anhydrous salt ; that any solution of a hydrated salt contains no 
hydrate of that salt, but that it is at the moment of crystallization that 
^combination of the water and salt takes place. 

IV. Vapoiir Pressures of Salt Sohdions. 1. Boiling Points of 
Saturated Solutions.^ 

The method of experiment was to measure the pressure under which 
■a saturated solution of the salt boiled at a definite temperature. 
The experiments included determinations at 65°, 75°, 85°, and 95° for 
NaNOs, KNO3, NagCOa, K2CO3, MnS04, FeS04, and the results are 
-expressed in terms of degrees of rise of boiling point. This is found 
to be a quantity increasing with the temperature when the solubility 
increases ; on the other hand, it decreases when the solubility diminishes 
with rise of temperature. 

It is preferable, however, to express the effect of salt on the 

» Published PMl. Mag., October 1885. 



VAPOUR PRESSURES AND REFRACTIVE INDICES OF SALT SOLUTIONS. 287 

1 — p^ 

vapour pressure of water by the value — i- ; where p = pressure of 

vapour of pure water, p^ := pressure of water vapour from salt solution 
containing 71 molecules per 100 H2O, and this, as was to be expected, is 
in all cases a diminishing quantity with rise of temperature — showing 
that, in a constantly saturated solution, a salt exercises a less restraining 
effect on the water the higher the temperature. 

2. Vapour Pressure of Water from Non-saturated Salt Solutions. 

The experiments on this subject are not yet complete, but are suffi- 
ciently advanced to justify certain conclusions regarding the behaviour 
of salts under varying conditions of temperature and concentration. 

The method employed was the same as that in the previous section, 
with this difference, that a dilute, not a saturated, solution of the salt 
was employed, and successive portions of water were distilled off and 
weighed. In this way the concentration at different pressures and at a 
definite temperature was readily determined. 

Four salts have, as yet, been examined, NaCl, KCl, NaNOg, and 
KNO3. The temperature chosen was 70°, though some experiments 
were made at 90°. 

Two of the above salts have been examined in solutions of constant 
strength at temperatures of 70°, 75°, 80°, 85°, and 90°. 

The general results are as follows : — 

(a) When temperature is constant and n varying, then P~P 

n 
increases with increase of n in the case of NaCl ; is constant, or nearly 
fio, with KCl, and diminishes more or less rapidly with NaNOg and 
KNO3. These results are fully confirmed by Tammann's results, obtained 
by the Barometric method (Wiedem. Ann. 24), a close agreement being 
found between the two sets of figures. 

(/3) When the concentration is constant but temperature varying, 

then the value of ^_i_ or 1 — ^ is a diminishing one with NaCI and 
pn pn 

a slowly increasing one in the case of the other three salts. This also is 

confirmed by Tammann's results, and general agreement is to be found 

with the experiments of Legrand (18.35), conducted in an entirely 

different way. 

It is believed that there is an intimate connection between this 

behaviour of the salts and their solubility, but the discussion of this 

question is postponed till the results are more numerous and complete. 

V. Expansion of Salt Solutions. 

The dilatation of solutions containing definite numbers of molecules 
1, 3, 5, or 2, 4, 6, Ac, of NaCl, KCl, NaNOj, and KNO3, have been 
determined by means of specially constructed dilatometers, and a special 
constant temperature bath, by means of which a tube 700mm. lono- can 
be kept for any length of time at a definite temperature, the tempera- 
ture of the one end differing from that of the other not more than 0°-l. 
Thus all necessity for correction of the results for the exposed portion of 
the stem of the dilatometer is avoided. 

As in the previous section, the experiments are not yet complete, but 
have fully established the following conclusions : — 



288 EEPOBT— 1885. 

(a) The expansion of a salt solution is the more nniform the more 
concentrated it is. The curves representing the expansion approach more 
nearly straight lines as n increases. 

(/3) At low temperatures salt solutions expand more than water, at 
higher ones less ; there is thus a point at which the coefficient of expan- 
sion is the same as that of water. This temperature is little, if at all^ 
affected by the concentration. They are as follows : — 



NaCl 


. 55°- 60° 


KCl 


. 50°- 55° 


NaNOa • 


. 80° -100° 


KNO3 . 


. 75°- 80° 



(y) The volumes at different temperatures may be satisfactorily ex- 
pressed by interpolation formulte of the form 

V= 100,000 + ra + i'2/3; 

Where t'=t°—20°, and a and /3 constants depending on the salt and the- 
value of n. In 126 determinations only two differed from the calculated 

value by more than ., ~.^^ , the mean error being less than ~^ 

100,000 ^ 100,000 

The constants a and /3 are thus related ; as n increases a increases, but /3 
decreases ; the expansion approximating more and more to 100,000 + a t'^ 
The results confirm in most points those of Kremers, and it is hoped 
when the experiments are complete that it will be possible to establish the- 
connection between the vapour pressures and the molecular volumes, aa 
has already been attempted by Tammann in an incomplete form. 



Rejport of the Committee, consisting of Professor Sir H. E. RoscoE, 
Mr. J. N. LocKYER, Professors Dewar, Wolcott Gibbs, Liveing, 
Schuster, and W. N. Hartley, Captain Abney, and Dr. Marshall 
Watts {Secretary), appointed for the purpose of preparing a new 
series of Wave-length Tables of the Spectra of the Elements and 
Compounds. 

The present Report contains the completion of the tables of the spectra 
of the elements, and a portion of those of the spectra of compounds. 
The measurements are given in ten-millionths of a millimetre (or tenth- 
metres), and are based upon the measurements of the Fraunhofer lines 
by Angstrom for the whole visible rays, and the extension of the same 
series of measurements into the ultra-violet portion of the spectrum made 
by Cornu and other observers. It will be well to repeat here the funda- 
mental values of wave-length of the chief solar lines. The small correc- 
tions indicated at page 29 of Angstrom's Memoir, ' Le Spectre Normal 
du Soleil,' have been applied to his numbers — but they are uncorrected 
for the dispersion of air. Hence the numbers in the tables represent 
wave-lengths in air, of 760°^™ pressure at Upsala, and 16° C. temperature. 
The numbers taken from Thalen's 'Determination des Longueurs d'Onde 
des Raies Metalliques ' in the same way have had applied to them the- 
necessary small corrections to bring them into harmony with the numbers 
finally adopted by Angstrom as ' Yaleurs definitives ' (pp. 25 and 31-32). 



ON WAVE-LENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 289 



Feaunhofbb Lines 



A . 

B . 

C (H). . 

D (Na) 

E (Ca & Fe) 

b, (Mg) . 

\ (Mg) . 

b3 (Ni & Fe) 

b, (Mg&Fe) 

F (H) 

G (Fe) 

H (Ca) 

K (Ca) 

L (Fe) 

M (Fe) 

N (Fe) 

O (Fe, double) 

P (Fe & Ti) 

Q (Fe) 

E (Fe & Ca) 

r (Fe, double) 

S, (Ni, double) 

Sj (Fe, triple) 

s (Fe) 

T (Fe, double) 

t (Fe) 

U (Fe) 



5892-12 



76040 
68670 
65621 
/ 5895-13 
\ 588912 
5269-13 
5183-10 
5172-16 
5168-48 
5166-88 
4860-72 
4307-25 
3968-1 
3933-0 
3819-8 
3727-0 
3580-5 
3439-8 
3359-2 
3284-9 
3179-0 
3144-3 
3100-6 \ 
3009-5/ 
3046-4 
3019-7 
2994-3 
2947-8 



3100-0 



The following symbols are employed in the tables to indicate the 
character of the lines : 

s denotes that the line is sharply defined. 

n denotes that the line is ill-defined or nebulous. 

b denotes a band, the position of the brightest part being given. 

b' denotes a band sharply defined on the least refracted side, and fading away 

towards the blue, 
b' denotes a band sharply defined on its more refracted side, and fading away 

towards the red. 

The width of a broad band is sometimes indicated by a suffix, giving 
the width in ninth-metres; thus, 4997 Vj means that the bright edge of 
the band is the 4997, and that it fades away above 4947 ; whereas 6532 b4 
means that the band extends from 6552 to 6512, its brightest point being 
at 6532. 

denotes that the line is continuous. 

d denotes that the line is discontinuous, or a ' short * line. 

r denotes that the line is frequently ' reversed.' 

A number within parentheses, thus : (3091-9), means that while a Une in this 

position has been observed, no new measurements of wave-length was made 

— the wave-length being quoted from another observer. 

The intensities of the lines are expressed upon an ascending scale 
from 1 to 10 ; 1 being the feeblest and 10 the brightest. 



1885. 



290 



EEPOET 1885. 



WAVE-LENGTH TABLES OF THE SPECTRA OF 
THE ELEMENTS. 

Sulphur. 



I. Band 
Spectrum 




II. Line 


Spectrum 


Intensity 
and Character 


Salet 


o 
Angstrom 


Hasselberg 


PlUcker and 

Hittorf 


i 
Salet 


I. 


II. 








6579 






2 








6454 






2 








6421 






4 








6404 


6400 




8 








6390 


6390 




6 








6321 


6325 




8 








6309 


6310 




8 








6290 


6290 




10 


6145 






6152 




lb' 


2 


6090 






6111 




lb- 


2 


6030 






6009 




lb- 


4 


5970 










2b' 




5900 






6866 




2b' 


4 


6845 






5810 




2b' 


4 


5780 






6780 




2b' 


4 


5715 










2b' 






5671 




5667 




■5670 




6 






5659-7 


5657 
5650 




5660 
5655 




8 
8 


5645 


5645 


5639-3 


5641 
5618 


a * 


5647 


3b' 


10 
4 




5613 


5603-8 


5609 




5610 




10 


5595 






5584 




3b' 


4 






5561-3 


5568 
5558 


5570 




8 
4 


8535 




5516-9 


5532 
5522 




3b' 


2 
4 






5507-3 


5.508 


5510 




8 


5480 










3b' 






5474 


5470-5 


5473 


f 5477 




8 




5451 


54510 


5452 


fi< *5455 




10 




5432 


5438-1 


5438 


L 5432 




8 


5425 




5429-7 
5418-4 
5386-6 


5425 




3b' 


6 


5365 










5b' 






5345 


5341-7 


5338 


f5350 




10 


6310 


5322 


5319-2 

5217-8 


5304 
5269 
5231 
5218 


^ L5320 


2b' 


10 
2 
4 
2 


6250 


5207 




5207 


/5220-| 
L5217 U 


8b' 


8 

8 


6190 


6191 


5214-4 
52001 


5199 
5191 
5182 


5205 J 
5160 


8b' 


10 

2 

10 


5143 




5142-5 


5143 
5141 




2b' 


6 
2 








5140 








2 



ON "WAVE-LENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 291 

Sulphite — cantinued. 



1 

I. Band 
Spectrum 


II. Line Spectrum 


Intensity 
and Character 


Salet 


o 
Angstrom 


Hasselberg 


Pliicker and 
Hittorf 


Salet 


I. 


IL 








5124 






4 








5110 






2 


5088 




6102-9 
5078.3 


5096 
5068 


5103 


8b' 


8 
2 


5040 




5044-9 


5044 
5036 




Sb" 


4 
2 




5027 


5032-5 


/5030 
1.5024 




f5030 
5024 




10 

10 




5013 


5012-7 


f5013 




5013 




8 








\ 5004 
5003 


e 


6008 




8 
2 


4990 


4994 


4993-9 


roOOO 
\4990 




5O0O 


6b' 


4 










.4990 




6 


4945 




4941-5 


4942 




6b' 


4 




4926 


4925 

4918-5 

4901-9 


4924 
4922 
4902 


C4925 




8 
6 
6 


4890 




4884-5 


4884 




2b 


6 


4840 






4825 


4825 


8b' 


6 






4815-6 


4813 


7?4810 




8 






4808-5 


4804 






4 


4793 




4792-8 
4778-5 
4762-8 
4752-8 


4791 
4777 
4768 
4762 




7b' 


4 
2 

2 
2 


4755 






4734 
4723 




2b' 


2 

2 






4714-9 


4718 


04715 




8 


4705 






4692 
4671 


4690 
4670 


5b' 


b 
b 


4655 






4657 
4630 


4655 
4630 


6b' 


b 
b 


4615 






4610 
4593 
4580 
4561 


4610 
4590 
4580 
4560 


8b' 


b 

b 
b 
b 






4551-5 


4552 




4556 




10 


4540 












2b' 








4524-7 


4323 




4525 




10 






4485-1 


4485 


M' 


4485 




10 


4470 












8b' 








4464-0 


4466 




4467 




10 


4450 






4432 
4422 


4435 

4425 


2b 


b 
b 


4367 






4386 
4358 
4330 
4343 
4336 
4329 


4390 


3b 


b 
4 
4 
4 
4 
4 


4320 










2b 










4315 




4315 1 




b 



U2 



292 



REPORT — 1885. 
Sulphur — oontimied. 



I. Band 
Spectrum 


II. Line Spectrum 


Intensity and 
Character 


I. Band 
Spectrum 


II. Line Spectrum 


Intensitj' and 
Character 


Salet 


Plucker i c„, . 
& Hittorf S*^^^* 


I. 


II. 


Salet 


Plucker 
& Hittorf 


Salet 


I. 


II. 




4297 
4284 
4279 
4272 
4259 
4255 
4241 
4229 


T< 


4295 

4282 

4269 
.4250 




8 

8 

4 

8 

4 

8 
b 
b 


4187 
4070 


4196 

4181 
4168 
4158 
4140 


4192 

f 4180 

p{ 4162 

L4155 


2b 

2b 


b 

6 
8 
6 
6 

2^ 



* Double. 

Tantalum. 



Arc Spectrum 


Intensity 

and 
Character 


Arc Spectrum 


Intensity 

and 
Character 


Arc Spectrum 


Intensity 

and 
Character 


Lockyer 


Lockyer 


Lockyer 


.3998-6 
3995-7 
3995-0 
3991-0 
3987-4 
3979-7 




3975-5 
39730 
3971-6 
3971-2 
3964-5 
3963-3 




3942-7 
3940-3 
3936-3 
3914-0 
39110 
390G-9 





Tellurium. 



I. Band 
Spectrum 


II. Line Spectrum 


Intensity an 


d Character 


Salet 


Salet 


Huggins 
6645 


Thale'n 


I. 












4 




(6437) 


6431 
6366 
6347 
6290 


6437-2 




10s 
Is 
In 
2? 


6250 




6243 
6228 




5b 


3n 
3s 


6150 








5b 




6050 


(6046) 


6042 


6046-2 


5b 


6sd 




(6012) 


6010 
5995 


6012-7 




6sd 
In 




(5973) 


5970 


5973-2 




lOsc 


5940 


(5935) 


5934 


5935-2 


5b 


8sc 




(5856) 


5854 


5856-6 




4sd 


5855 


(5852) 


5849 


5852-1 


7b 


4sd 




(5825) 




5825-1 




4nd 




(5805) 




5805-6 
5781-1 




4nd 

6sd 




(5755) 


5756 


57551 




lOsc 






5740 


5741-1 




2sd 


5735 








8b' 






(5707) 


5708 


5706-6 




lOsc 


5685 








8b 






(5647) 


5646 


5647-1 




lOsc 






5618 


5616-1 




4sd 




(5574) 


5675 


5574-1 




8sc 


5560 








4b 






(5488) 


5486 


54880 




6sd 



ON "WAVE-LENGTH TABLES OF THE SPECTRA OF THE ELEMENTS. 293 

Tellurium — continued. 



I. Band 
Spectrum 


II. Line Spectrum 


Intensity and Character 


Salet 


Salet 


Huggins 


Thale'n 


I. 


n. 


5470 


(5477) 


5476 


5477-6 


4b 


6sd 




(5447) 


5447 


5447-6 




Ssc 


5410 




5409 


5408-6 


4b 


4sd 




(5366) 


5366 


53661 




6sc 


5340 








4b 






(5310) 


5309 


5310-1 




6sd 






5298 


52991 




2sd 


5278 








4b 




5220 


(5217) 


5222 


5217-2 
5172-2 


4b 


8nc 
2sd 


5156 


(5152) 




5152-2 


4b 


6sd 






5134 


5133-2 




2nd 




(5104) 




5104-1 




6sd 


5070 








4b 








5038 


5035-1 




4sd 


5015 








4b 




4970 








4b 




4920 






4895-1 


4b 


2nd 


4870 


(4866) 


4866 


4866-6 


4b 


4nd 






4832 


4832-1 




2nd 


48-W 








4b 




^o—v 


Hartley 


4785 


4785-1 


2nd 


4767 


and Adeney 






8b 




4725 








8b 






4707-5 


4709 






4sd 




46930 








4sd 


4670 




4664 
4652 




8b 


In 
In 


4600 


4602-0 


4602 
4599 


4603-6 


6b 


2sd 
In 


4560 




4544 




6b 


b 


4510 


/4487-0 
\ 4480-0 






6b 


2sd 




4479 






2sd 


4470 


4436-0 






4b 


2sd 


4400 


44000 
4378-0 
4364-5 






4b 


2sd 
2sd 
2sd 


4350 


43530 


4352 




2b 


2.sd 


4330 


4324-6 






2b 


4sd 




4301-5 


4302 






6sd 


4280 


r4292-7 

\ 4287-3 

4274-4 






2b 


4sd 
4sd 
6sd 




4259-8 


4259 






6sd 


4250 


4221-1 






2b 


6sd 


4200 


r 4180-7 
\4170-3 






2b 


2sd 
4sd 


4150 


4119-7 
4072-7 






2b 


4sd 
2sd 




4061-3 


4063 






Csd 



294 



RBPORT 1885. 



Tellurium — continued. 



Line Spectrum 


Intensity 

and 
Character 


Line Si)ectrum 


Intensity 
and 

Character 


Line Spectrum 


Intensity 

and 
Character 


Hartley 


Hartley 


Hartley 


and Adeney 




and Adeney 




and Adeney 


^I^A-AlrAA lt,V^bX^4 


4054-2 


6sd 


332:>7 


4sd 


2923-4 


4sd 


4048-3 


4sd 


3315-8 


4sd 


2918-9 


2sd 


4006-0 


8sd 


3307-1 


8sc 


2905-9 


2sd 


3983-8 


6sd 


3289-6 


2sc 


2901-9 


4sd 


3968-6 


6sd 


/ 3280-0 


lOsc 


/2894-3 
\ 2893-3 


Snd 


3948-0 


6sd 


1.3273-4 


lOsc 


6sd 


3932-5 


2sd 


/ 3267-4 
\ 3264-6 


2sd 


/ 2877-4 
\ 2873-6 


2sd 


3908-7 


2nd 


2sd 


2sd 


3841-3 


8sd 


3256-3 


Ssd 


f2867-7 
s' 2859-9 
[28570 


Snd 


3803-0 


4sd 


3250-8 


4sd 


6sd 


3796-9 


2sd 


3216-8 


lOsc 


Snd 


3789-0 


4sd 


32421 


4sd 


/ 2844-9 
1 2840 


6sd 


3776-0 


4sd 


; 3234-2 


4sd 


6sd 


3771-0 


4sd 


\ 3229-4 


2sd 


; 2836-9 
12834-4 


2sd 


3765-0 


4sd 


3221-8 


4sd 


2sd 


37590 


4sd 


3217-6 


4sd 


2823-2 


6sc 


3754-0 


4sd 


3213-3 


4sd 


[2815-3 


2sd 


3735-5 


Ssd 


3210-4 


2sd 


\28130 


2sd 


3726-2 


Ssd 


3192-2 


4sc 


f 2799-1 


4sd 


37160 


4sd 


3188-1 


4sc 


■{ 2795-6 


4sd 


3698-7 


4sd 


3183-7 


2sd 


L2791-9 


Snd 


3683-3 


4sd 


3174-4 


4sc 


f 2768-6 


6sc 


3676-7 


4sd 


3168-5 


4sd 


<^ 2766-5 


6sd 


3670-4 


4sd 


3158-4 


2sd 


[ 2766-0 


4sc 


3656-4 


4sd 


3154-1 


4sd 


2756-0 


2sc 


/ 3649- 2 
\3644-3 


6sd 


3145-7 


4sd 


2751-5 


2nd 


6sd 


3131-7 


2sd 


r2745-0 
\2743-0 


4sd 


3636-3 


4sd 


3124-7 


2sd 


4sd 


3626-7 


4sd 


3119-5 


4nd 


/ 2739-5 
L 2738-0 


4sd 


3617-0 


6sd 


3107-5 


6sd 


4sd 


3611-0 


4sd 


3098-7 


4sd 


f 2723-2 
■{ 2720-7 
L27I8-O 


2nd 


3601-7 


4sd 


3095-5 


4sd 


2sd 


3599-6 


4sd 


308S0 


4sd 


2sd 


35